U.S. patent number 4,912,475 [Application Number 07/330,976] was granted by the patent office on 1990-03-27 for techniques for determining orbital data.
This patent grant is currently assigned to Massachusetts Institute of Technology. Invention is credited to Charles C. Counselman, III.
United States Patent |
4,912,475 |
Counselman, III |
March 27, 1990 |
Techniques for determining orbital data
Abstract
Techniques are disclosed for determining orbital data of space
borne vehicles including earth satellites such as those of the
NAVSTAR Global Positioning System. Each of a set of such satellites
transmits signals which include carrier waves which may be
suppressed, or only implicity present. The signals are received
from the observable satellites concurrently by means of an antenna
at each of at least three ground stations forming a network of
baselines. The stations are arrayed such that the ratio of the
maximum to the minimum baseline length is much greater than one.
From the signals received at a station pair forming each baseline a
time series of doubly-differenced phase measurement data is formed
which is biased by an integer number of cycles of phase. The data
series for different satellite and station pairs are processed
together to determine the orbits of the satellites and the
doubly-differenced phase biases. Unique determination of the
integer values of at least some of the biases is facilitated by the
above noted spatial arrangement of the stations such that the ratio
of the maximum to the minimum baseline length is much greater than
one. This integer bias determination enhances the accuracy of the
related orbit determination. Unique determination of the integer
values of at least some of the doubly-differenced carrier phase
biases may also be facilitated by the use of a plurality of carrier
frequencies with the ratio of the maximum to the minimum frequency
being much greater than one.
Inventors: |
Counselman, III; Charles C.
(Belmont, MA) |
Assignee: |
Massachusetts Institute of
Technology (Cambridge, MA)
|
Family
ID: |
26704002 |
Appl.
No.: |
07/330,976 |
Filed: |
March 29, 1989 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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28712 |
Mar 20, 1987 |
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Current U.S.
Class: |
342/352; 342/424;
701/531 |
Current CPC
Class: |
G01S
3/48 (20130101); G01S 5/02 (20130101); G01S
19/02 (20130101); G01S 19/44 (20130101) |
Current International
Class: |
G01S
1/00 (20060101); G01S 3/48 (20060101); G01S
5/14 (20060101); G01S 3/14 (20060101); G01S
5/02 (20060101); H04B 007/185 (); G01S 005/02 ();
G01C 021/00 () |
Field of
Search: |
;342/352,356,357,358,424
;364/459 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
King et al., Surveying with GPS, Monograph, No. 9, School of
Surveying, Univ. of New South Wales, 1985. .
Bossler et al., Using the Global Positioning System for Geodetic
Positioning, pp. 553-563, Bull. Geod. 54 (1980). .
W. N. Christensen and J. A. Hogbom, Chap. 7, Entitled "Aperture
Synthesis", pp. 171-189, of Book Entitled "Radiotelescopes",
Published in 1969 by the Cambridge University Press, England. .
A. E. E. Rogers, "Very Long Baseline Interferometry with Large
Effective Bandwidth for Phase Delay Measurements", Radio Science,
vol. 5, No. 10, pp. 1239-1247, Oct., 1970. .
A. E. E. Rogers, "Broad-Band Passive 90.degree. RC Hybrid with Low
Component Sensitivity for Use in the Video Range of Frequencies",
Proceedings of the IEEE, vol. 59 (1971), pp. 1617-1618. .
C. C. Counselman, III and I. I. Shapiro, "Miniature Interferometer
Terminals for Earth Surveying," Proceedings of the Second
International Symposium on Satellite Doppler Positioning, vol. 11,
pp. 1237-1286, Jan. 1979, Available from the University of Texas at
Austin. .
C. C. Counselman, III, I. I. Shapiro, R. L. Greenspan & D. B.
Box, Jr., "Backpack VLBI Terminal with Subcentimeter Capability",
National Aeronautics & Space Admin. Conference Publication
2115, Entitled "Radio Interferometry Techniques for Geodesy", pp.
409-414, Published in 1979. .
C. C. Counselman, III et al., "Very Long Baseline Interferometric
Geodesy with GPS Satellites", Proposed to NASA, Jul., 1980. .
Ron Hatch, "The Synergism of GPS Code and Carrier Measurements",
Proceedings of Third International Geodetic Symposium on Satellite
Doppler Positioning, vol. 2, pp. 1213-1231, Presented in Feb. of
1982 by the Physical Science Laboratory of the New Mexico State
University. .
G. Beutler, D. A. Davidson, R. B. Langley, R. Santerre, P. Vanicek
and D. E. Wells, "Some Theoretical and Practical Aspects of
Geodetic Positioning Using Carrier Phase Difference Observations of
GPS Satellites", Published in Jul. 1984 as Technical Report No. 109
of Department of Surveying Engineering, of the University of New
Brunswick, Canada. .
R. I. Abbot, Y. Bock, C. C. Counselman, III, R. W. King, S. A.
Gourevitch and B. J. Rosen, Entitled "Interferometric Determination
of GPS Satellite Orbits", Proceedings of the First International
Symposium on Precise Positioning with the Global Positioning
System, vol. 1, pp. 63-72, Published May 1985 by the National
Geodetic Information Center, National Oceanic and Atmospheric
Administration, Rockville, Md., 20852, U.S.A. .
G. Beutler, W. Gurthner, I. Bauersima and R. Langley, Entitled
"Modeling and Estimating the Orbits of GPS Satellites", Proceedings
of the First International Symposium on Precise Positioning with
the Global Positioning System, vol 1, pp. 99-112, Published May
1985 by the National Geodetic Information Center, National Oceanic
and Atmospheric Administration, Rockville, Md, 20852, U.S.A. .
Bock et al., "Establishment of Three-Dimensional Geodetic Control
by Interferometry with the Global Positioning System", JGR, vol.
90, No. B9, pp. 7689-7703, Aug. 10, 1985. .
R. W. King, E. G. Masters, C. Rizos, A. Stolz and J. Collins,
Monograph, No. 9, Entitled "Surveying with GPS", Published by the
School of Surveying, The University of New South Wales, Kensington,
N.S.W. 2033, Australia, Nov. 1 .
The U.S. government has rights in this invention pursuant to
Contract Number F19628-86-K-0009 awarded by the Department of the
Air Force..
|
Primary Examiner: Tarcza; Thomas H.
Assistant Examiner: Issing; Gregory C.
Attorney, Agent or Firm: Morgan & Finnegan
Government Interests
The U.S. government has rights in this invention pursuant to
Contract Number F19628-86-K-0009 awarded by the Department of the
Air Force.
Parent Case Text
This is a continuation of co-pending application Ser. No. 028,712,
filed Mar. 20, 1987, abandoned July 25, 1989.
Claims
What is claimed is:
1. A method of determining orbital data from doubly differenced
phase observations of satellites derived from stations defining a
network of baselines, comprising:
(a) arranging the stations to provide a wide ranging progression of
baseline lengths, from short to long;
(b) applying observations from a long baseline to enhance
observations from a substantially shorter baseline by resolving
ambiguity in said short baseline observations;
(c) applying the enhanced observations from the short baseline to
enhance observations from a longer baseline by resolving ambiguity
in said longer baseline observations; and
(d) applying the enhanced observations to enhance the orbital data
determination.
2. The method of claim 1, wherein:
a plurality of said satellites transmit code-modulated,
spread-spectrum, suppressed-carrier signals simultaneously on the
same frequencies; and
the phase observations are related to a plurality of carrier waves
implicit in the signals received at each station and are derived
from these signals independently of externally derived knowledge of
the information content of the codes modulating these carriers.
3. The method of claim 2, further comprising:
using an upward looking omnidirectional antenna at a station to
collect a first composite signal simultaneously including
overlapping spread-spectrum signals received from a plurality of
satellites;
reconstructing the first composite signal to form a second
composite signal simultaneously including a discrete reconstructed
carrier component from each of the plurality of satellites;
using Doppler differences to separate reconstructed carrier
components corresponding to the same implicit frequency transmitted
by different satellites; and
measuring the phases of the separated reconstructed carrier
components of a plurality of satellites simultaneously.
4. The method of claim 2, further comprising:
deriving phase observations related to a plurality of implicit
carriers having a first frequency and a substantially different
second frequency in the transmissions of each satellite, said first
and second frequencies being the same for different satellites;
and
using phase observations related to the second frequency to enhance
observations related to the first frequency by resolving ambiguity
in the latter observations.
5. The method of claim 1, further comprising:
arranging the stations to provide a wide ranging progression of
baseline projections on two orthogonal axes.
6. The method of claim 1, further comprising:
arranging the stations to provide a geometric progression of
baselines.
7. The method of claim 5 or 6, further comprising:
arranging the stations to provide redundant baselines.
8. The method of claim 1, further comprising:
applying modulation delay observations of the satellites to enhance
the orbital data determination.
9. The method of claim 8, further comprising:
applying modulation delay observations of the satellites to enhance
ambiguity resolution.
10. An improved method of determining orbital data from doubly
differenced phase observations of satellites derived from stations
defining a network of baselines, wherein the improvement
comprises:
(a) arranging the stations to provide a wide ranging progression of
baseline lengths, from short to long;
(b) applying observations from a long baseline to enhance
observations from a substantially shorter baseline by resolving
ambiguity in said short baseline observations;
(c) applying the enhanced observations from the short baseline to
enhance observations from a longer baseline by resolving ambiguity
in said longer baseline observations; and
(d) applying the enhanced observations from the longer baseline to
enhance the orbital data determination.
11. The method of claim 10, wherein:
a plurality of said satellites transmit code-modulated,
spread-spectrum, suppressed-carrier signals simultaneously on the
same frequencies; and
the phase observations are related to a plurality of carrier waves
implicit in the signals received at each station and are derived
from these signals independently of externally derived knowledge of
the information content of the codes modulating these carriers.
12. The method of claim 11, further comprising:
using an upward looking omnidirectional antenna at a station to
collect a first composite signal simultaneously including
overlapping spread-spectrum signals received from a plurality of
satellites;
reconstructing the first composite signal to form a second
composite signal simultaneously including a discrete reconstructed
carrier component from each of the plurality of satellites;
using Doppler differences to separate reconstructed carrier
components corresponding to the same implicit frequency transmitted
by different satellites; and
measuring the phases of the separated reconstructed carrier
components of a plurality of satellites simultaneously.
13. The method of claim 11, additionally comprising:
deriving phase observations related to a plurality of implicit
carriers having a first frequency and a substantially different
second frequency in the transmissions of each satellite, said first
and second frequencies being the same for different satellites;
and
using phase observations related to the second frequency to enhance
observations related to the first frequency by resolving ambiguity
in the latter observations.
14. The method of claim 10, further comprising:
arranging the stations to provide a wide ranging progression of
baseline projections on two orthogonal axes.
15. The method of claim 10, further comprising:
arranging the stations to provide a geometric progression of
baselines.
16. The method of claim 14 or 15, further comprising:
arranging the stations to provide redundant baselines.
17. The method of claim 10, further comprising:
applying modulation delay observations of the satellites to enhance
the orbital data determination.
18. The method of claim 17, further comprising:
applying modulation delay observations of the satellites to enhance
ambiguity resolution.
Description
TABLE OF CONTENTS
1. Background of the Invention
1.1. Field of the Invention
1.2. The Global Positioning System
1.2.1. GPS Satellite Orbits
1.2.2. Transmitted Signals
1.2.2.1. Carriers and Modulation
1.2.2.2. Carrier Reconstruction
1.3. Deriving Position Information from GPS Signals
1.3.1. Using Carrier Phase
1.3.1.2. Ambiguity Resolution
1.3.1.3. Effect of Orbital Uncertainty
1.3.1.4. Avoiding Ambiguity Resolution
1.3.1.5. Orbit Determination
2. Summary of the Invention
3. Brief Description of the Drawings
4. Detailed Description of Preferred Embodiment
FIG. 1. System of Stations Linked to Data Processor
FIG. 2. Tracking Station
FIG. 3. Receiver
FIG. 4. Tracking Channel
FIG. 5. 616 f.sub.0 Detector
FIG. 6. Range Generator
1. BACKGROUND OF THE INVENTION
1.1. Field of the Invention
This invention relates to improved techniques for determining
orbital data of space traveling objects such as earth satellites,
and more particularly to improved radio interferometric methods and
instrumentation for determining such data.
Orbital data are data representative of the path of a satellite in
space and, more specifically, of the position of a satellite at a
particular time or as a function of time. Orbital data may
represent an orbit in various ways. For example, a satellite's
position and velocity vectors may be specified in rectangular
coordinates at a certain epoch. Alternatively, the elements of an
osculating or a mean ellipse may be given.
Radio interferometric data such as differences of carrier phase
observations of satellite signals from a pair of receiving stations
constitute a kind of orbital data. However, the present invention
concerns the combination of carrier phase data from three or more
receivers and the processing of the combined data to determine data
more directly representative of the path or position of a satellite
in space. Therefore, the term "orbital data" will be used herein to
refer to the latter data, and the term "orbit determination" will
be used to refer to the process of deriving such orbital data from
the phase measurement data.
Although the invention is disclosed with reference to the
satellites of the NAVSTAR Global Positioning System, or "GPS", it
applies as well to the determination of orbital data of other space
traveling, radio transmitting objects, such as the Soviet GLONASS
satellites and certain other space craft.
1.2. The Global Positioning System
The GPS is now in the process of being deployed by the U.S.
Department of Defense, and will be used mainly for purposes of
navigation and position determination. About seven satellites of
the GPS now orbit the earth and transmit radio signals by which
users can determine their positions on earth.
1.2.1. GPS Satellite Orbits
When complete, the Global Positioning System is expected to include
about 21 satellites orbiting the earth in three planes. About seven
satellites will be distributed around a geocentric circular orbit
in each of these planes; each plane will be inclined to the earth's
equator by an angle of about 55 degrees; and the equator crossing
points, or nodes, of the orbits will be about equally spaced in
longitude, about 120 degrees apart.
The altitudes of the orbits above the surface of the earth are all
about 20,000 km, and the common orbital period is about 24 hours as
viewed from the rotating earth. Thus, the GPS satellites are not
"geostationary", but each appears to a ground-based observer to
rise, move through the sky, and set daily. From any given point on
the earth's surface, at least four satellites will be in view at
any time, 24 hours per day. Because the orbits are so high, a given
satellite at a given time may be seen from widely separated points
on the earth's surface.
1.2.2. Transmitted Signals
Each GPS satellite transmits microwave L-band radio signals
continuously in two frequency bands, centered at 1575.42 MHz and
1227.60 MHz and known as the "L1" and the "L2" bands, respectively.
Within each of these GPS bands, the transmitted signal is a
broadband, noise-like, pseudorandom signal which contains no
discrete spectral components. The signals are therefore said to be
carrier-suppressed.
1.2.2.1. Carriers and Modulation
The term "carrier" is used herein in the same sense as is usual in
the radio art; that is, a carrier is a periodic wave of essentially
constant amplitude, frequency, and phase. Information may be
conveyed, or "carried" by varying the amplitude, frequency and/or
phase of such a signal. A carrier may be called a "subcarrier" if
its frequency is less than the bandwidth of the signal. A signal
may include several carriers. For example, a broadcast television
signal is said to include a video carrier and an audio carrier.
Although no carriers are present in the GPS signals as transmitted,
various carriers may be said to be implicit therein, in that such
carriers may be recovered or reconstructed from the GPS
signals.
Within each GPS satellite, a stable frequency standard such as an
atomic cesium beam device provides a fundamental frequency of 5.115
MegaHertz, called f.sub.0, from which all other critical satellite
frequencies are derived by integer multiplication or division. The
frequency of the L1band center frequency carrier of GPS signals is
308 times f.sub.0 or 1575.42 MegaHertz, and the frequency of the L2
band center frequency carrier is 240 times f.sub.0 or 1227.60
MegaHertz. The f.sub.0 fundamental frequency is a carrier frequency
which may be reconstructed from the GPS signals.
GPS signals are bi-phase or quadriphase modulated. In particular,
quadrature components of an L band center frequency carrier are
multiplied, in the satellite, with pseudorandom, binary valued
waves m(t) and n(t). The m(t) and n(t) waveforms are aperiodic, but
periodic carrier waves are implicit in them. Polarity or phase
reversals of m(t) and n(t) occur only at times which are integer
multiples of fixed time intervals tm and tn known as the chip
widths of m(t) and n(t), respectively.
If m(t) reversed Polarity at every multiple of tm, then m(t) would
be a periodic square wave with a frequency equal to 1/(2tm).
Because the polarity reversals actually occur pseudorandomly, just
half the time on average, the 1/(2tm) frequency carrier wave is
suppressed, as is the band center frequency carrier.
Similarly, if n(t) reversed polarity at every multiple of tn, then
n(t) would be a periodic square wave with a frequency equal to
1/(2tn). Again, because n(t) reverses polarity pseudorandomly, both
the 1/(2tn)-frequency carrier and the band center frequency carrier
are suppressed.
In each GPS satellite's transmitter, one quadrature component of
the 308 f.sub.0 or 1575.42 MHz, L1 band center frequency carrier is
modulated with m(t), which has chip width tm equal to 5/f.sub.0 or
about 977.5 nanoseconds. The orthogonal component of the L1 band
center frequency carrier is modulated with n(t), which has chip
width tn equal to 1/(2f.sub.0) or about 97.75 nanoseconds. The 240
f.sub.0 or 1227.60 MHz, L2 band center frequencY carrier is
modulated with only n(t). Thus, in the spread spectrum signal
transmitted in the L1 band, at least three different carrier waves
are implicitly present, with frequencies of f.sub.0 /10 (equal to
0.5115 MHz), f.sub.0 (equal to 5.115 MHz), and 308 f.sub.0 (equal
to 1575.42 MHz). In the spread spectrum signal transmitted in the
L2 band, at least two different carrier waves are implicitly
present, with frequencies of f.sub.0 (5.115 MHz) and 240 f.sub.0
(1227.60 MHz).
Other carrier frequencies may also be implicit in the GPS signals.
For example, the m(t) wave is itself the product of several waves
whose time intervals between polarity reversals are fixed integer
multiples of tm. Thus, additional carriers whose frequencies are
corresponding submultiples of 1/(2 tm) are implicitly present. One
of the waveforms or factors multiplied together to produce m(t),
known as the "C/A" code waveform or C/A code sequence, is a
satellite-specific, pseudorandom, binary sequence of 1023 chips
repeated periodically with a period of 1 millisecond, or a
frequency of 1 kiloHertz.
Another factor in m(t) is a stream of binary "navigation" data
having a 20-millisecond chip width, thus a 25 Hertz carrier
frequency. These data include the current time indicated by the
satellite's clock, a description of the satellite's current
position in orbit, and a description of corrections to be applied
to the time indicated by the satellite's clock. These data are
broadcast by the satellites for use in the process of determining
the position of a receiver from measurements of the received
signals. Similar or identical data may be included in the n(t) wave
which may modulate both the L1 and the L2 band center frequency
carriers.
1.2.2.2. Carrier Reconstruction
Various techniques are known for reconstructing carrier waves from
the spread spectrum signal received from a GPS satellite. In the
conventional technique, the received signal is multiplied by a
replica, generated locally, of the satellite-specific C/A code
waveform present in m(t), or of the "P" or "Y" code which is
present in n(t). In other techniques, no code sequence is generated
in the receiver. Such codeless techniques may be utilized when the
relevant code is unknown or to avoid code dependence.
An aspect of some carrier reconstruction techniques, including the
codeless technique used in the preferred embodiment of the present
invention described hereinbelow, is that the second harmonic rather
than the fundamental frequency of an implicit carrier is
reconstructed. In the preferred embodiment, second-harmonic
frequencies of 616 f.sub.0 and 2 f.sub.0 are reconstructed from the
GPS signals received in the L1 band, and frequencies of 480 f.sub.0
and 2 f.sub.0 are reconstructed from the signals received in the L2
band.
1.3. Deriving Position Information from GPS Signals
Various methods are known for deriving position information from a
signal received from a GPS satellite. In some methods, the time
delay of the pseudorandom code modulation of the signal is
measured. In others, the phase of a periodic carrier wave implicit
in the signal is measured. Time delay and carrier phase
measurements may be combined. In any case, information relating
both to the position of the receiver and to the position of the
orbiting satellite is obtained. The present invention is primarily
concerned with the determination of orbital position
information.
1.3.1. Using Carrier Phase
The position information obtainable by measuring the phase of a GPS
carrier wave, especially one of the relatively short wavelength, L1
or L2 band center frequency carriers, is potentially much more
accurate than the information obtainable by measuring the
modulation delay. However, the potential accuracy of carrier phase
information can be difficult to achieve because carrier phase
measurements are ambiguous. Their full potential cannot be realized
unless the ambiguity problem can be resolved.
Because resolving phase ambiguity is an important aspect of the
present invention, this problem and known methods of attacking or
avoiding it are reviewed hereinbelow. The ambiguity problem is a
fundamental one affecting all types of phase measurements, but its
nature and the difficulty of solving it depend strongly on the
techniques used to collect and process the measurements. The nature
of the ambiguity problem, whether it can be solved, and if so how,
depend particularly on how well the positions of the satellite and
the receiving station are known. Uncertainty in knowledge of a
satellite orbital position causes more serious difficulty in
solving the ambiguity problem than uncertainty in a fixed receiver
position.
Which position is unknown is critical because, for example, a fixed
receiver position may be specified for the entire time span of an
extensive set of observations, by the values of just three
coordinates (for example, latitude, longitude, and height). On the
other hand, a minimum of six parameters must be specified to define
the orbit of a satellite, even for a relatively short time
span.
Techniques are known for solving the carrier phase ambiguity
problem in determining unknown receiver coordinates, but only when
the relevant satellite orbital parameters are relatively well
known. The most efficient techniques known for receiver position
determination rely on a method of phase data processing known as
"double differencing". In double difference phase processing, as
described below, the problem of resolving carrier phase ambiguity
appears as a problem of determining integer numbers called
ambiguity parameters.
The present invention addresses the problem of phase ambiguity in
the context of determining unknown orbital parameters. This
problem, as mentioned, is much more difficult than the ambiguity
problem in determining unknown receiver position coordinates.
To determine unknown orbital parameters, it is known to use double
difference phase processing. When this is done, however, the
orbital uncertainty interferes with determination of the integer
values of the ambiguity parameters. Because the ambiguity
parameters cannot be determined, in other words because the
ambiguity of carrier phase is not resolved, the accuracy of the
orbit determination is degraded.
The difficulty of resolving phase ambiguity in the orbit
determination process is such that the usually recommended
procedures do not include any attempt to resolve phase
ambiguity
The present invention enables more accurate orbit determination by
improving the ability to resolve phase ambiguity in the process. As
an aid to understanding the invention, known methods of resolving
ambiguity, usable in the determination of an unknown receiver
position when orbits are already accurately known, are reviewed
hereinbelow. Why known methods of resolving ambiguity fail when the
orbits are unknown is also discussed.
1.3.1.1. Double Differencing
As mentioned, it is known to determine the position of a receiver
by measuring the phase of a carrier wave implicit in signals
received from a GPS satellite. The most accurate methods involve
comparing the phases of the carrier waves of signals received
simultaneously from different satellites. Carrier waves (or their
second harmonics) are reconstructed from the received signals, and
the phases of these carriers are measured with respect to a local
reference oscillator in the receiver. The carrier phase measurement
data are processed to determine position coordinates of the
receiver.
Known methods of processing address the fact that carrier phase
measurements are corrupted by additive biases. The biases stem from
three sources: (1) The measured phase includes the phase of the
transmitting oscillator in the satellite. This phase is not only
random; it varies randomly with time. (2) The phase of the
receiver's local oscillator has been subtracted from the measured
phase. This phase also varies randomly with time. (3) In addition,
the measured phase is biased by an unknown integer number of cycles
because a carrier wave is a periodic wave. This integer cycle bias
represents the inherent ambiguity of a carrier phase
measurement.
Carrier phase measurements are ambiguous because a carrier wave is
a periodic wave. One cycle of any periodic phenomenon is, by
definition, indistinguishable from any other cycle. By observing a
periodic wave such as a reconstructed GPS carrier signal
continuously, one can determine its phase changes unambiguously.
The total value of a phase change, including both the integer
number of cycles and the additional fraction of a cycle, can be
observed. However, without more information one cannot determine
the initial value of the phase.
Because the initial value is unknown, a continuous series of phase
measurements has an unknown, constant bias. As long as the bias is
unknown, useful information can not be derived from the average, or
mean, value of the series of measurements. Although useful
information is contained in the variation about the mean, the mean
value will only contain useful information if the bias can be
determined.
The bias of a series of carrier phase measurements stemming from
the phase of any given satellite's oscillator may be cancelled by
subtracting measurements of that satellite's signal made
simultaneously at two different receiving stations. The resulting
between-stations difference observable is still useful for
determining the position of one receiver if the position of the
other is known.
The bias of a series of carrier phase measurements stemming from
the phase of any given receiver's oscillator may be cancelled by
subtracting simultaneous measurements by that receiver of two
different satellites. The resulting between-satellites difference
observable is still useful for determining the position of the
receiver.
Biases related to both kinds of oscillators are canceled if both
types of differencing are employed: between stations and between
satellites. This is known as double-differencing, or doubly
differenced phase processing.
The double differencing method requires a plurality of satellites
to be observed simultaneously at each of a plurality of receiving
stations. At each station, carriers are reconstructed from the
received signals, and the carrier phases are measured with respect
to the local reference oscillator, for all the satellites at the
same time. Then differences are taken between phases measured for
different satellites at the same time, in order to cancel the
common errors associated with the local oscillator phase.
Carrier phase measurements from three or more receivers at a time
may be combined in a double-differencing mode. If at a specific
epoch, n receivers observed m satellites, then (n-1)(m-1) linearly
independent double differences can be formed. An efficient
algorithm for combining carrier phase data from more than two
receivers is described in the article by Yehuda Bock, Sergei A.
Gourevitch, Charles C. Counselman III, Robert W. King, and Richard
I. Abbot, entitled "Interferometric Analysis of GPS Phase
Observations", appearing in the journal manuscripta geodaetica,
volume 11, pages 282-288, published in 1986. As disclosed
hereinbelow, the present invention involves the combination, in a
doubly differenced mode, of measurements made by three or more
receivers.
1.3.1.2. Ambiguity Resolution
An important consequence of the cancellation of transmitter and
receiver oscillator phase contributions in doubly differenced phase
measurements is that the constant bias of a continuous measurement
series (due to ignorance of the initial value) is an integer number
of cycles of phase. Sometimes the value of this integer can be
determined, so that distance- or other position-related information
can be derived from the average value of a series of measurements.
The process of determining the integer value of the bias of a
series of phase measurements is called "resolving the ambiguity" of
the series.
Because doubly differenced phase ambiguity resolution is an
essential part of the present invention, the concept will be
reviewed further as an aid to understanding the invention. The
following review uses the notation and some of the language of an
article by G. Beutler, W. Gurtner, M. Rothacher, T. Schildknecht,
and I. Bauersima, entitled "Using the Global Positioning System
(GPS) for High Precision Geodetic Surveys: Highlights and Problem
Areas", appearing in the IEEE PLANS '86 Position Location and
Navigation Symposium Record, pages 243-250, published in 1986 by
the Institute of Electrical and Electronics Engineers, New York.
For clarity, many details are omitted here.
Let L represent the wavelength of a reconstructed carrier wave,
that is, the speed of light c divided by the reconstructed carrier
frequency. In the case of a receiver which reconstructs the second
harmonic of an implicit carrier frequency, the wavelength is
computed from twice the implicit carrier frequency.
Let r.sup.i.sub.k represent the distance or "range" between
receiver k at the reception and measurement time, t, and satellite
i at the time of transmission, (t-r.sup.i.sub.k /c).
Let f.sub.k represent the phase of the k.sup.th receiver's local
reference oscillator, and let f.sup.i represent the phase of the
i.sup.th satellite's transmitting oscillator.
Then the so-called "one way" phase observable f.sup.i.sub.k, for
the signal received from the i.sup.th satellite at the k.sup.th
receiver, is given theoretically by the equation
where all phases are expressed in cycles and N.sup.i.sub.k is an
integer expressing the intrinsic ambiguity of this phase
observable.
Four one-way phases measured at the same epoch t, at a pair of
receiving stations k and q and for pair of satellites i and j, are
differenced to form a doubly differenced observable:
Again, subscripts denote receivers and superscripts denote
satellites. The double differencing cancels the transmitter and the
receiver oscillator phases. The effects of the differences between
the satellite-to-receiver distances, and a bias which is an integer
number of cycles, remain:
Here, DDr.sup.i.sub.k.sup.j.sub.q is the doubly differenced range,
and N.sup.i.sub.k.sup.j.sub.q is the integer bias, sometimes called
the "ambiguity parameter".
Determining uniquely the true integer value of the unknown bias of
a continuous series of doubly-differenced phase observations is
called "resolving the ambiguity" of the series. If the ambiguity
parameter of a series can be determined, it may be subtracted from
each observation in the series, or otherwise accounted for. Then
useful information may be derived from the average value of the
series of measurements. Thus, the value of an observation series is
enhanced by determination of the bias.
In general, a series of observed values of doubly-differenced phase
is composed of a mean, or average, value, plus a variation about
the mean. Both the mean value and the variation about the mean
contain potentially useful information about the positions of the
satellites and the receivers. The mean value of the phase is
related to the mean of the doubly-differenced satellite-receiver
distance, and the variation of the phase is related to the
variation of this distance.
If the mean value includes an additive bias which is unknown, then
one does not know the value of the position-related part, so it is
difficult to derive meaningful position information from the mean
value. However, once the additive bias is known, the
position-related part of the mean value of the observed phase is
known and can contribute to determining the positions of the
receivers.
If the positions of the satellites were unknown and the additive
bias could be determined, the mean value of the observed phase
could contribute to determining the positions of the satellites.
Determining the additive bias and applying the mean value
information to determine the positions of satellites is an aspect
of the present invention.
One method of determining the integer bias of a series of
doubly-differenced phase observations is simply to utilize
sufficiently accurate information from an external source to
calculate the value of the phase observable with an uncertainty of
less than one-half cycle. A simple example of using information
from an external source would be the use of independently derived
information about the positions of the satellites and the stations
to calculate the doubly differenced range,
DDr.sup.i.sub.k.sup.j.sub.q, in Eq. 3. Substituting the actually
observed value of the doubly differenced phase for the theoretical
value, DDf.sup.i.sub.k.sup.j.sub.q, in Eq. 3 yields an equation
which may be solved for the ambiguity parameter,
N.sup.i.sub.k.sup.j.sub.q.
Another example of using independently derived information to
determine the ambiguity parameter is the use of a "parallel" series
of doubly-differenced observations, from the same pair of stations
and for the same pair of satellites, and at one or more of the same
measurement epochs, of the satellite-to-station path length as
inferred from the time delay of the code modulation of a satellite
signal. This method was proposed in a paper published in 1979 by C.
C. Counselman III, I. I. Shapiro, R. L. Greenspan, and D. B. Cox,
Jr., entitled "Backpack VLBI Terminal with Subcentimeter
Capability", appearing in National Aeronautics and Space
Administration Conference Publication 2115, "Radio Interferometry
Techniques for Geodesy", on pages 409-414. A detailed development
of this method was given in a paper by Ron Hatch, entitled "The
Synergism of GPS Code and Carrier Measurements", appearing in the
Proceedings of the Third International Geodetic Symposium on
Satellite Doppler Positioning, volume 2, pages 1213-1231, published
in 1982 by the Physical Science Laboratory of the New Mexico State
University.
This method relies on the ability to determine the
doubly-differenced range from observations of the modulation delay
with sufficiently small uncertainty that the bias of the
doubly-differenced center frequency carrier phase for the same
station pair and satellite pair is computable with less than
one-half cycle of error. An important aspect of this method is that
it does not require determination or external knowledge of the
geometry. The satellite-to-receiver distance, whatever its value,
delays the signal modulation and the center-frequency carrier by
the same amount. Therefore the ability to resolve ambiguities by
this method is essentially independent of uncertainty in available
knowledge of the station positions and the satellite orbits.
Unfortunately, it has proven extremely difficult in practice to
measure the modulation delay of the signal with sufficient accuracy
to ensure correct resolution of the L band center-frequency carrier
phase ambiguities, and the utility of this method has so far been
rather limited.
Related methods of resolving ambiguities in phase observations of
GPS satellites are known in which phases are observed for a
plurality of reconstructed carriers including one or more
subcarriers. The phase of a subcarrier is indicative of modulation
delay.
Methods of resolving ambiguities in which carrier phase
observations are made at up to about ten different frequencies,
including some closely spaced frequencies, some widely spaced
frequencies, and some progressively spaced intermediate
frequencies, are also known, as proposed for example by C. C.
Counselman III and I. I. Shapiro in the paper entitled "Miniature
Interferometer Terminals for Earth Surveying" published in the
Proceedings of the Second International Symposium on Satellite
Doppler Positioninq, Vol. II, pp. 1237-1286, January 1979,
available from the University of Texas at Austin. This method is
akin to the method of bandwidth synthesis employed for the
unambiguous measurement of delay in very long baseline radio
interferometry, as described in a publication by A. E. E. Rogers,
entitled "Very Long Baseline Interferometry with Large Effective
Bandwidth for Phase Delay Measurements", appearing in Radio
Science, vol. 5, no. 10, pages 1239-1247, October 1970.
Simultaneous observation of different frequencies, and/or the
combination of code delay and carrier phase measurements, is also
known to be useful for the purpose of determining, and thereby
eliminating, the frequency-dependent effects of ionospheric
refraction on the satellite signals.
The known multiple-frequency and bandwidth synthesis methods are
very much like the above mentioned GPS code-delay method; all are
independent of, and do not involve knowledge or determination of,
the satellite-station geometry. Unfortunately, the signals
transmitted by the GPS satellites are not really suitable for use
of the multiple-frequency and bandwidth synthesis methods. A
serious problem is that the widths of the GPS L1 and L2 bands are
too small in comparison with the frequency spacing between the
bands. It is the relatively narrow GPS signal bandwidth which also
severely limits the utility of the code-delay method. The reasons
behind the limitation are related.
As discussed herein below, the determination of satellite orbital
data in accordance with the present invention involves the use of
at least three receiving stations preferably including some closely
spaced stations, some widely spaced stations, and stations with a
progression of intermediate spacings. The spacings in this case
refer to geometrical distance. However, an analogy exists between
the use of progressively spaced stations and the use of
progressively spaced frequencies. Although it may not be feasible
to equip the GPS (or any other) satellites to transmit a suitable
progression of frequencies, it is indeed feasible to set up an
array of tracking stations with a suitable progression of
geometrical spacings. In a sense, therefore, the present invention
may be said to compensate for the gaps in the GPS frequency
spectrum which limit the use of known multi-frequency and related
techniques.
Similarly, where a system provides a suitable spacing of frequency
components, the dependence on varied base line lengths is
reduced.
Of all known methods of resolving ambiguity in doubly-differenced
phase observations, probably the most useful, and therefore most
widely used in determining unknown station position coordinates
when satellite orbital parameters are sufficiently accurately known
a priori, is to estimate the ambiguity parameters and the station
coordinates simultaneously by least-squares fitting to the
doubly-differenced phase observations.
In this method the information which is contained in the variation
about the mean of each series serves, in effect, to determine the
unknown position-related quantities; from the determinations of
these quantities the satellite-to-station path lengths are
computed; the computed Path lengths are converted from distance to
phase units by dividing by the wavelength, and are doubly
differenced; the mean of the doubly differenced phase thus computed
is subtracted from the actually observed mean; and the resulting
difference is an estimate of the bias. Ideally this estimate is
near an integer value and has sufficiently small uncertainty that
the correct integer value of the bias can be identified with
confidence.
In an extension of this method, every integer value in a finite
interval surrounding the estimate of each ambiguity parameter (one
for each continuous series of observations) is tested by repeating
the least-squares adjustment, or "fit", of all the non-ambiguity
parameters to the observations for each trial set of integer values
of the ambiguity parameters. For each trial, the sum of the squares
of the post-fit differences, or "residuals", between the observed
and the corresponding computed values of doubly differenced phase
is computed. This sum, which the least-squares fitting process
attempts to minimize, indicates the badness of the fit. The
particular set of integer values of ambiguity parameters found to
have the smallest sum of squares of post-fit residuals is
identified. Confidence in the correctness of this identification is
indicated by the contrast between the related sum of squares, and
the next-smallest sum or sums.
Ambiguity resolution by methods such as these is known to be useful
in the processing of carrier phase data when the errors in the
theoretically computed values of the phase observables are small in
comparison with one cycle of phase. Obviously, if the magnitudes of
these errors can approach or exceed one-half cycle, they can
prevent the correct determination of the ambiguity parameters. It
is known that such errors increase with increasing distance between
a pair of receivers. The magnitudes of the phase errors are known
to increase with increasing distance between the receiving stations
for several reasons.
1.3.1.3. Effect of Orbital Uncertainty
One of the most important reasons is that an error in the assumed
knowledge of a satellite's orbit causes an error in the
theoretically computed value of a between-stations satellite range
difference, such as Dr.sup.i.sub.kg for satellite i and stations k
and q, which is proportional to the distance between stations k and
q. The magnitude of the error is about equal to the inter-station
distance multiplied by the orbital error measured in radians of arc
as subtended at the midpoint of the baseline (and also as projected
in a direction parallel to the baseline in question).
Thus, for example, if the orbital error as seen from a baseline on
the ground and in the direction of the baseline is 2.times.10-7
radian, then the error in the computed value of Dr.sup.i.sub.kg
will be 1 centimeter for a 50-kilometer distance, and 10
centimeters for a 500-kilometer distance. For observations of the
L1 band center frequency carrier, which has a wavelength of about
19 cm, a 2.times.10-7 radian orbital error would probably not cause
trouble in the ambiguity resolution process for a 50-km baseline.
However, it might for a 500-kilometer baseline.
In general, it is known to use ambiguity resolution when the orbits
of the satellites are known a priori with sufficient accuracy, and
the distance between receivers is sufficiently short, that the
phase error related to the orbital error is small in comparison
with one-half cycle and therefore does not interfere with correct
integer-cycle bias determination.
It is known to determine the orbits of GPS satellites by Processing
doubly-differenced phase observations. But in this processing, as
far as is known, doubly-differenced phase ambiguity resolution has
not been practiced. The practice of doubly-differenced phase
ambiguity resolution has been limited to the determination of
unknown receiver positions when the orbits of the satellites have
been known a priori with sufficient accuracy. Heretofore, whenever
satellite orbits have been substantially unknown a priori, and
doubly-differenced phase observations have been processed to
determine the orbits, the unknown phase biases or ambiguity
parameters have been estimated as real-number (i.e., numerically
continuous, as opposed to integer or discrete-valued) unknowns
along with the unknown orbital parameters.
Because the sensitivity of the between-stations differenced phase
observable to orbital error increases with increasing distance
between stations, it is known to use observations from receiving
stations separated by the greatest possible distances in order to
obtain the most accurate orbit determination. It is customary to
use observations from stations separated by thousands of
kilometers.
1.3.1.4. Avoiding Ambiguity Resolution
At least two methods of handling ambiguity parameters as continuous
variables, rather than integers, are known. In both methods the
variables representing the ambiguity, or continuous unknown bias,
parameters, are real numbers like the variables representing the
satellite orbits, etc. One method is to solve for the unknown
ambiguity-related variables explicitly. That is, they are
determined by solving a large set of simultaneous equations
explicitly including all of the unknown variables. This solution
yields estimates of the biases as well as estimates of the other
unknowns. Performing such a simultaneous solution was the first
step in one of the ambiguity resolution methods described
above.
Another method avoids the whole matter of ambiguity parameters. In
this method, known as the "implicit bias" method, the biases are
eliminated, or solved for only "implicitly", by redefining the
observable quantities so that they have no biases. Each series of
doubly-differenced phase observations for a given station pair and
satellite pair is replaced by itself minus the arithmetic mean, or
average, value of the original series. If DDf(t.sub.i) represents
the doubly-differenced phase observation at the i.sup.th epoch
t.sub.i, the new, unbiased observation DDf'(t.sub.i) is given
by
This bias-cancelling operation is performed separately for each
doubly-differenced observation series, that is, for each
station/satellite pair. Now, ambiguity parameters do not appear at
all in the set of equations which is solved to determine the
orbital parameters, etc.
In this method, all position related information contained in the
mean value of the original series of observations is thrown away
when the mean is subtracted. Of course, the information is also
wasted in the "explicit" bias determination method if the biases
are treated as real numbers and never fixed at their integer
values, i.e. if the ambiguities are not resolved. The advantage of
the "implicit" method, if the ambiguities are not going to be
resolved anyway, is a simplification of the computations, due to
the reduction of the number of unknowns to be solved for.
Although there are great differences between the explicit and the
implicit methods with respect to practical matters such as computer
size, speed, and precision requirements, there is no theoretical
difference between these methods regarding the accuracies of the
non-bias parameter determinations, provided of course that
ambiguity resolution is not considered. Because ambiguity
resolution is generally not considered in GPS orbit determination,
Beutler and others have recommended the implicit-bias method of
processing doubly differenced phase measurements for orbit
determination.
1.3.1.5. Orbit Determination
The use of doubly-differenced phase observations for GPS satellite
orbit determination is disclosed in an article by R. I. Abbot, Y.
Bock, C. C. Counselman III, R. W. King, S. A. Gourevitch, and B. J.
Rosen, entitled "Interferometric determination of GPS satellite
orbits", appearing in the Proceedings of the First International
Symposium on Precise Positioning with the Global Positioning
System, vol. 1, pages 63-72, published in 1985 by the National
Geodetic Information Center, National Oceanic and Atmospheric
Administration, Rockville, Md., 20852, U.S.A.
The principles and the practice of GPS satellite orbit
determination from doubly differenced carrier phase data are
further disclosed in an article by G. Beutler, W. Gurtner, I.
Bauersima, and R. Langley, entitled "Modeling and estimating the
orbits of GPS satellites", appearing in pages 99-112 of the same
Proceedings volume, and in an article by G. Beutler, D. A.
Davidson, R. B. Langley, R. Santerre, P. Vanicek, and D. E. Wells,
entitled "Some theoretical and practical aspects of geodetic
positioning using carrier phase difference observations of GPS
satellites", published in 1984 as Technical Report No. 109 of the
Department of Surveying Engineering, of the University of New
Brunswick, Canada.
The refinement of station position coordinates and a priori
satellite orbital parameters by adjusting both simultaneously to
fit doubly-differenced phase observations has also been disclosed,
for example in the paper by Gerhard Beutler, Werner Gurtner, Markus
Rothacher, Thomas Schildknecht, and Ivo Bauersima, entitled
"Determination of GPS Orbits Using Double Difference Carrier Phase
Observations from Regional Networks", appearing in the Proceedings
of the Fourth International Geodetic Symposium on Satellite
Positioning, volume 1, pages 319-335, published in 1986 by the
Applied Research Laboratories of the University of Texas at
Austin.
However, the utilization of ambiguity resolution in GPS satellite
orbit determination is not known. When the orbits have been
substantially uncertain, specifically when the combination of
orbital uncertainty and inter-station distance yields phase bias
uncertainty approaching or exceeding one-half cycle, then it is not
known how to determine the bias parameters with uncertainty small
enough to permit unique identification of their integer values. If
the explicit solution method is used to estimate the biases
simultaneously with the orbital parameters, one tends to find that
the uncertainties of the bias estimates are not much smaller than
one cycle.
Analysis reveals that the relatively large uncertainties in the
estimates of the bias parameters when these parameters are
estimated simultaneously with orbital parameters results from the
fact that a change in the estimate of a bias parameter may be
masked very effectively by certain kinds of changes in the
estimates of the unknown orbital parameters. That is, the orbit may
be adjusted in a certain way, and the bias parameters also changed,
such that the net effects on the calculated values of the
doubly-differenced phase observables are less than the measurement
uncertainties. In other words, it is theoretically possible to
shift the orbit such that the observable quantity changes by a
nearly constant amount--which resembles the effect of a change in
the bias.
Accordingly, it is said that the bias parameters are difficult to
separate from the orbital parameters. It is also said that the bias
parameters are correlated with the orbital parameters. The
difficulty of separating biases from orbital parameters is greater
if the time span of the observations is shorter. However, the
difficulty is substantial even if a satellite is observed for the
duration of its visible "pass", from horizon to horizon. The
difficulty is such that ambiguity resolution has not been
considered feasible in the context of orbit determination.
From the difficulty in separating the bias and the orbital
parameters, it follows that if some way could be found to determine
uniquely the integer values of the biases, then the orbital
parameters could be determined more accurately.
2. SUMMARY OF THE INVENTION
It is a general object of the present invention to provide an
improved method for determining the orbits of satellites. A more
specific object is to enhance the determination of the orbits of
satellites by determining uniquely the integer cycle values of the
biases of doubly-differenced phase observations of the satellites
derived from ground stations and processed to determine the orbits
of satellites.
In accordance with the techniques of the present invention, each of
a set of such satellites transmits radio signals including carrier
waves which may be suppressed, or only implicitly present. The
signals are received from the observable satellites concurrently by
means of an antenna at each of at least three ground stations. The
relative position vector extending from one receiving station to
another is called a "baseline vector", or simply a "baseline", and
the distance between the stations is called the baseline length. A
network of baselines is said to connect the stations. The stations
are arrayed such that the ratio of the maximum to the minimum
baseline length is much greater than one.
At the same time at each station, carrier phase measurements are
made of the signals received from each observable satellite. The
measurements are repeated at a series of such times while the
satellites move substantial distances in their orbits.
For each observation at a particular station, the phase
measurements are differenced between satellites. The
phase-difference data at that station are also differenced with the
phase difference data derived concurrently at another station and
from the same observed satellites, to form a set of
doubly-differenced phase data in which the contributions of
station-specific and satellite-specific phase errors have been
cancelled.
As a consequence, a time series of doubly-differenced phase
measurement data is formed which is biased by an integer number of
cycles of phase. This series is combined with a series of data from
a different baseline, or station pair, and the two data series are
processed together to determine the orbits of the satellites. The
doubly-differenced phase biases are determined simultaneously with
the orbits. Unique determination of the integer values of at least
some of the biases is facilitated by the above noted spatial
arrangement of the stations wherein the ratio of the longest to the
shortest baseline length is much greater than one. This integer
bias determination enhances the accuracy of the related orbit
determination.
It should be noted that the deliberate use of closely spaced ground
stations for orbit determination is contrary to conventional wisdom
which teaches that the stations should be as far apart as possible
in order to obtain maximum "leverage". The sensitivity of a
doubly-differenced phase observable to any orbital parameter, or
mathematically speaking the partial derivative of the observable
with respect to the orbital parameter, is known to be approximately
proportional to the distance separating the relevant pair of
stations. However, the magnitudes of the errors present in such an
observation do not increase so rapidly with increasing distance
between the stations. Therefore the "signal to noise ratio" of the
observations is increased, i.e. improved, by increasing the
distance. Usually one seeks to maximize the distance, subject to
the constraints of economics, politics, geography, and the limited
region of mutual visibility of the relevant satellites.
The methodology of the present invention involves a kind of
bootstrapping, or positive feedback, which occurs in the
determination of the integer biases when closely and widely spaced
stations are used together. If the bias of a series of
doubly-differenced phase observations is unknown, then the usable
information content of the series resides only in the
time-variation of the series of observed values. This
time-variation information from the observations derived from the
most widely spaced stations serves to determine the orbits with
sufficiently small uncertainty that the integer biases of other
observation series, from closely spaced stations, can be determined
uniquely.
The unique determination of these integers enhances the value of
the observations from these closely-spaced stations. With their
integer biases having been determined, and removed or accounted
for, the doubly-differenced phase observations from the more
closely spaced stations yield additional information, contained in
their average value. This average-value information is in addition
to the information contained in the time variation. The
average-value information is not available until and unless the
bias is removed, because otherwise the unknown bias masks the
average value.
The enhancement of the closer-station observations enables the
orbital parameters to be determined more accurately, with the
result that it becomes possible to determine uniquely the integer
biases of observations from more widely spaced stations. The
consequent enhancement of these more-widely-spaced-station
observations enables the orbital parameters to be determined still
more accurately, with the result that it becomes possible to
determine the integer biases of observations from still more widely
spaced stations, and so on until all biases have been determined
uniquely. However, it should be noted that the orbit determination
may still be enhanced substantially even if some of the integers
remain undetermined, that is, if the integer values of some of the
biases are not uniquely determined. It should also be noted that
while it is useful to conceptualize the invention as a succession
of bootstrapping refinements, in actual practice it may be
preferable to process all observations, from all stations,
simultaneously in order to determine many or all of the bias
parameters simultaneously.
Analysis of the present concept for resolving ambiguity by
combining observations from different inter-station spacings
reveals analogies to the method of eliminating ambiguity proposed
by C. C. Counselman III and I. I. Shapiro in the paper entitled
"Miniature Interferometer Terminals for Earth Surveying" published
in the Proceedings of the Second International Symposium on
Satellite Doppler Positioning, Vol. II, pp. 1237-1286, January
1979, available from the University of Texas at Austin, and the
method of eliminating ambiguity in the determination of delay in
very long baseline radio interferometry, as described in a
publication by A. E. E. Rogers, entitled "Very Long Baseline
Interferometry with Large Effective Bandwidth for Phase Delay
Measurements", appearing in Radio Science, vol. 5, no. 10, pages
1239-1247, October 1970. However, the use of observations from one
interferometer baseline, i.e. one pair of stations, to resolve
ambiguity in the observations from another baseline is not
suggested in these publications. In the ambiguity resolution
methods described in both of these publications, observations are
combined from a wide range of frequencies (or frequency spacings)
for a single baseline, rather than from a wide range of geometrical
spacings.
An analogy to the present concept for resolving ambiguity by
combining observations from different inter-station spacings may
also be found in the method of synthesizing a directional antenna
beam pattern by combining individual antenna elements having a wide
range of geometrical spacings, as described for example by W. N.
Christiansen and J. A. Hoghom in Chapter 7, "Aperture synthesis",
pages 171-189, of the book entitled "Radiotelescopes", published in
1969 by the Cambridge University Press, England.
Unique determination of the integer values of at least some of the
doubly-differenced carrier phase biases in accordance with the
present invention may be facilitated by the use of a plurality of
carrier frequencies with the ratio of the maximum to the minimum
frequency being much greater than one.
As previously noted, and where the satellite carrier frequencies
permit, phase measurements of the signals received from each
satellite simultaneously at each station may be made for a
plurality of carrier frequencies with the ratio of the maximum to
the minimum frequency being much greater than one. Determination of
the integer values of at least some of the doubly-differenced
carrier phase biases is facilitated by the use of such frequencies
and thus enhances the accuracy of the orbit determination.
This second, multi-frequency, aspect of the invention, used either
separately or together with the first mentioned, multi-spacing
aspect, is related to the first aspect in a way which may be
appreciated by considering that the sensitivity of the
doubly-differenced phase observable to an orbital parameter is
proportional not only to the spacing of the stations, as mentioned
above, but also to the carrier frequency of the observations.
Therefore the sensitivity of the phase observable, measured in
cycles, is proportional to the spacing measured in wavelengths at
the observing frequency. Thus there is a parallel between (1)
exploiting a multiplicity of spacings, and (2) exploiting a
multiplicity of frequencies.
The parallelism is not exact because various sources of error in
the observations, especially ionospheric refraction error, will
scale somewhat differently in the two cases. Still, the use of
widely separated carrier frequencies has an effect substantially
similar to that of using a wide range of inter-station
spacings.
Just as the use of a closely spaced pair of stations in conjunction
with a widely spaced pair facilitates the unique determination of
the integer values of the biases of doubly-differenced carrier
phase biases, so does the use of a low carrier frequency or a
closely spaced pair of carrier frequencies in conjunction with a
high carrier frequency or a widely spaced pair of carrier
frequencies. Preferably, the use of a multiplicity of station
spacings is combined with the use of a multiplicity of frequencies,
or frequency spacings.
3. BRIEF DESCRIPTION OF THE DRAWINGS
Serving to illustrate an exemplary embodiment of the invention are
the drawings wherein like reference numerals represent like
parts:
FIG. 1 illustrates a system for determining orbits of GPS
satellites using reconstructed carrier phase measurements of
signals received at ground stations.
FIG. 2 illustrates a block diagram of a station for receiving GPS
signals and making reconstructed carrier phase measurements thereof
in accordance with the system shown in FIG. 1.
FIG. 3 illustrates a receiver for use in the station shown in FIG.
2.
FIG. 4 illustrates one of the tracking channels used in the station
shown in FIG. 2.
FIG. 5 illustrates one of the synchronous detectors used in the
tracking channel shown in FIG. 4.
FIG. 6 illustrates the range generator used in the tracking channel
shown in FIG. 4.
4. DETAILED DESCRIPTION OF PREFERRED EMBODIMENT
FIG. 1
Referring now to FIG. 1, a system is shown in accordance with a
preferred embodiment of the present invention for determining the
orbits of a plurality of GPS satellites, illustrated by GPS-12 and
GPS-14 in geocentric orbit 20, and GPS-16 and GPS-18 in geocentric
orbit 22. The satellites are currently visible at stations STN-30,
STN-32, STN-34, STN-36, and STN-54 on Earth 10.
Radio signals 24 continuously transmitted by each satellite are
concurrently received by means of an antenna, not shown in FIG. 1,
at each station STN-30, 32, 34...54. (Only those signals received
at STN-32 are illustrated).
Although two satellites, GPS-12 and GPS-14, are illustrated in one
orbital plane 20 and two other satellites, GPS-16 and GPS-18, are
illustrated as orbiting in another plane 22, other satellite
configurations may be treated in accordance with the present
invention as long as two or more satellites are simultaneously
visible at two or more ground stations, to permit
double-differencing of simultaneous phase observations.
It is not necessary, according to the method of the present
invention, for a given pair of satellites to be observed
simultaneously by different pairs of stations. Two series of
doubly-differenced observations, by different pairs of stations at
different times, may still be combined to determine the satellite
orbits in accordance with the method of the present invention
provided that the satellite orbital parameters are substantially
the same at the different times. Different pairs of satellites
might also be observed at different times by a given pair of
stations.
An array of thirteen stations is illustrated although, as
mentioned, a different number and/or a different arrangement
thereof may be used in accordance with the present invention. A
preferred arrangement of stations is drawn approximately to scale,
in plan view, and with orientation indicated by compass rose 26 in
FIG. 1. Only the plan view of the array is drawn with attention to
scale and orientation in FIG. 1, not the small squares marking the
stations themselves, the Earth, the satellites, etc. It is
understood that an actual array of stations on the surface of the
earth will generally not be exactly planar.
In the illustrated array, stations are arranged in a logarithmic
spiral with the ratio of the distances between successive pairs of
stations being equal to the square root of 2, about 1.4, and with
the vectors between successive pairs of stations being
perpendicular. Station STN-32 is about 453 kilometers west of
STN-30 and 320 kilometers north of STN-34. STN-36 is about 226
kilometers east of STN-34 and 160 kilometers south of STN-38.
STN-40 is about 113 kilometers west of STN-38 and 80 kilometers
north of STN-42. STN-44 is about 57 kilometers east of STN-42 and
40 kilometers south of STN-46. STN-48 is about 28 kilometers west
of STN-46 and 20 kilometers north of STN-50. STN-52 is about 14
kilometers east of STN-50 and 10 kilometers south of STN-54.
Stations STN-34, STN-42, STN-50, STN-54, STN-46, STN-38, and STN-30
lie along a straight line running from southwest to northeast.
Stations STN-32, STN-40, STN-48, STN-52, STN-44, and STN-36 lie
along a straight line running from northwest to southeast. The
distances of the stations from the center defined by the
intersection of these southwest-northeast and northwest-southeast
axes increase in a geometric progression.
Similarly, the east-west and the north-south inter-station spacings
are seen to increase in geometric progression. For example, the
north-south spacings are 10, 20, 40, 80, 160, and 320
kilometers.
Data communication link 60 carries phase measurement data from all
stations to data processor 62 where they are subject to
doubly-differenced processing to generate improved determinations
of the orbits of the satellites, represented for example by orbital
data 64. Data communication link 60 is illustrated as running
around the spiral from STN-54 to STN-52, thence to STN-50, and so
on through STN-30, to data processor 62. This has been done to make
apparent the logarithmic spiral arrangement of the stations. In
practice, however, another data communication route might be more
convenient. For example, data processor 62 could be located near
the center of the array, at the intersection of the
southwest-northeast and the northwest-southeast axes of the array,
and four data communication links running in straight lines
radially outward could connect data processor 62 to the stations.
Moreover, data processor 62 does not need to be separately located;
it can be located at one of the stations.
It is not necessary for data communication link 60 to be a
permanent or dedicated link, or for data communication to be
performed in real time. Phase measurement data generated at each
station may be stored locally and transferred whenever convenient
to data processor 62 for later processing. A convenient means for
such data transfer is the commercial switched telephone
network.
The preferred array size, with respect to the number of stations
and with respect to inter-station distance, is a function of
various considerations as discussed hereinbelow. Typically a
minimum distance of the order of magnitude of 10 kilometers and a
maximum distance of the order of several hundred kilometers will be
preferred if the L1 and L2 band center frequency carrier phases are
observed.
So long as appropriate baseline length ratios are observed, neither
the size nor the shape of the array is critical, and both aspects
may be varied to suit economic and geographic constraints. Provided
that the requirements for resolving ambiguities or "fixing
biases"are satisfied, better orbit determination accuracy will be
obtained if greater inter-station distances are used, and if the
distances projected in both of two perpendicular directions, e.g.
along north-south and east-west axes, are great. The minimum
inter-station distances, preferably as projected in both of two
perpendicular directions, should be sufficiently small that the
biases of the doubly-differenced phase observations from the most
closely spaced stations can be determined uniquely with a high
degree of certainty even under less than ideal conditions. The
progression of spacings, from minimum to maximum, preferably should
not include any ratio so large that biases can not be determined
uniquely for the next-larger spacing, given successful
determinations for the spacings up to that one.
Reliability is an important aspect of any orbit-determination
system. The reliability of accurate orbit determination in
accordance with the present invention is enhanced by arraying the
stations so that the failure to obtain valid phase observations
from any one station does not result in too large a gap in the
progression of available inter-station distances from minimum to
maximum. In this case, "too large" means that biases can not be
determined uniquely for the next-larger spacing, above the gap,
given successful determinations for the spacings below the gap. A
failure to obtain usable observations from a station might result
from an electrical or mechanical malfunction, or from severe local
weather which caused the refractivity of the atmosphere above the
station to be anomalous.
In this respect a log-periodic array such as the one illustrated in
FIG. 1 represents a relatively fault-tolerant, and therefore a
reliable, design. From the log-periodicity of this array it is
apparent that except for the inner and outer end stations STN-54
and STN-30, the failure of any one station does not result in the
total loss of any of the principal inter-station spacings, as
projected on north-south and east-west axes. For example, consider
station STN-38, which is located 113 kilometers east of STN-40 and
160 kilometers north of STN-36. East-west projected spacings of 113
kilometers are also provided by the pair, STN-34 and STN-42, and by
the pair STN-42 and STN-36. North-south projected spacings of 160
kilometers are also provided by the pair, STN-34 and STN-40, and by
the pair STN-40 and STN-32.
At a sacrifice in reliability, stations could be removed from the
array. The spacing ratio could also be increased, in order to
reduce the number of stations required to span the desired range of
spacings. The array illustrated represents a relatively
conservative, "belt and suspenders" design.
For the sake of reliability it is also desirable to provide
redundant or backup means for data communication link 60 and data
processor 62.
During operation of the system according to the present invention,
measurements are made simultaneously by equipment at each ground
station, as shown and discussed below with reference to FIG. 2, of
the reconstructed carrier phases of the signals 24 received from
each observable satellite GPS 12, 14, 18. The measurements are
repeated at a series of such times while the satellites move
substantial distances in their orbits.
It is convenient to govern the timing of the measurements at each
station by a local clock, as shown and discussed below with
reference to FIG. 2, which is synchronized with the clocks at the
other stations. Methods of achieving this synchronization by
reference to the signals received from one or more of the
satellites are known. Therefore, it is not necessary to transmit
time synchronization signals through data communication link 60,
although this is a possible means for synchronizing the
observations and may be preferred, for example, to simplify the
apparatus which must be provided at the stations.
The reconstructed carrier phase measurements are preferably carried
out in accordance with a regular schedule, such as once per minute,
every minute on the minute (as long as a satellite is visible), as
indicated by the local clock. In this manner it may be ensured that
all stations observe all visible satellites simultaneously.
Equipment suitable for use at a tracking station to receive the GPS
satellite signals, reconstruct carrier waves therefrom, and measure
the carrier phases without knowledge of the modulating codes is
available commercially and is described in the U.S. patent
application entitled "METHOD AND SYSTEM FOR DETERMINING POSITION ON
A MOVING PLATFORM, SUCH AS A SHIP, USING SIGNALS FROM GPS
SATELLITES", Ser. No. 852016, filed on Apr. 14, 1986, which
application is a continuation-in-part of the U.S. patent
application entitled "METHOD AND SYSTEM FOR MEASURING BASELINE
VECTORS BY RADIO INTERFEROMETRY USING RADIO SIGNALS FROM GPS
SATELLITES", Ser. No. 353,331, filed on Mar. 1, 1982. Both
applications are in the name of Charles C. Counselman III. Suitable
equipment which uses locally generated replicas of the GPS codes to
perform the same functions is also available commercially.
Data processor 62 is preferably a general purpose digital computer
suitable for scientific computation, such as one of the Digital
Equipment Corporation's VAX series of minicomputers.
Algorithms suitable for use in data processor 62 have been
described, for example, by R. W. King, E. G. Masters, C. Rizos, A.
Stolz, and J. Collins in Monograph No. 9, entitled "Surveying with
GPS", published by the School of Surveying, The University of New
South Wales, Kensington, N.S.W. 2033, Australia; by R. I. Abbot, Y.
Bock, C. C. Counselman III, R. W. King, S. A. Gourevitch, and B. J.
Rosen, in an article entitled "Interferometric determination of GPS
satellite orbits" appearing in the Proceedings of the First
International Symposium on Precise Positioning with the Global
Positioning System, vol. 1, pp. 63-72, 1985; and in an article by
Gerhard Beutler, Werner Gurtner, Ivo Bauersima, and Richard Langley
entitled "Modelling and Estimating the Orbits of GPS Satellites"
also appearing in the Proceedings of the First International
Symposium on Precise Positioning with the Global Positioning
System, vol. 1, pp. 99-112.
An efficient algorithm for processing the carrier phase measurement
data from all the stations simultaneously to determine the orbits
of the satellites is further described in the paper by Yehuda Bock,
Sergei A. Gourevitch, Charles C. Counselman III, Robert W. King,
and Richard I. Abbot, entitled "Interferometric Analysis of GPS
Phase Observations", appearing in the journal manuscripta
geodaetica, volume 11, pages 282-288, published in 1986.
As explained in the paper by Bock et al., the most efficient way to
combine phase data from an array of stations involves the
simultaneous processing of all observations which were made
simultaneously. That is, doubly-differenced phase observations are
not separately processed for separate pairs of stations, taken two
at a time, or for separate pairs of satellites, taken two at a
time. Similarly, the most efficient way to process phase data from
a plurality of carrier frequencies involves the simultaneous
processing of all observations, from all frequencies, together.
Accordingly, while the previously noted successive determination of
bias integer values is useful conceptually to understand the
invention, in actual practice the preferred procedure involves the
simultaneous estimation of all relevant parameters. In other words,
parallel processing is more efficient than serial.
FIG. 2
Referring now to FIG. 2, a block diagram is shown of one of the
stations STN-n of the set STN 30, 32, 34, 36, ... 54 at which the
signals from the plurality of GPS satellites are received and
reconstructed carrier phase measurements are made.
As illustrated in FIG. 1 and FIG. 2, each station STN-n receives
concurrently the signals transmitted by each of the GPS satellites
GPS-12, GPS-14, GPS-16 and GPS-18, such as signals 24 received from
satellite GPS-12. Through data communication link 60,
illustratively a commercial switched telephone network, station
STN-n communicates with data processor 62, shown in FIG. 1.
Station STN-n includes upward looking omni-directional antenna 100,
receiver 102, frequency standard 106, clock 108, a plurality of
identical tracking channels 112, computer 120, and modem 122.
Antenna 100, whose phase center is accurately known and positioned
with respect to a local geodetic monument, not shown, receives
simultaneously the signals transmitted by all satellites in view.
Antenna 100 is designed to respond to the signals received directly
from the satellites through free space, and to reject signals
scattered or reflected from nearby objects or surfaces such as the
ground below. Rejection of such scattered or reflected signals is
important to prevent them from altering the phases of the received
signals which ideally are just the directly received signals.
Because antenna 100 preferably receives signals from the sky and
not from the ground, it is called "upward looking". Because antenna
100 receives signals from all directions in the sky, it is also
called "omnidirectional". A type of antenna well suited for the
present application is disclosed in U.S. Pat. No. 4,647,942 issued
Mar. 3, 1987, entitled "CIRCULARLY POLARIZED ANTENNA FOR SATELLITE
POSITIONING SYSTEMS". The particular antenna disclosed in U.S. Pat.
No. 4,647,942 was designed to receive only one of the GPS bands,
the L1 band. A dual-band, L1 and L2, version of the antenna
disclosed in U.S. Pat. No. 4,647,942 is available commercially as
the antenna of the MACROMETER II.sup..TM. Interferometric Surveying
System. MACROMETER II is a trademark of Aero Service Division,
Western Geophysical Company of America. Antenna 100 is preferably a
MACROMETER II antenna or an equivalent.
In the system illustrated in FIG. 2, the relative-position or
"baseline" vectors between the phase centers of the antennas at all
of the stations, and also the position vector of the phase center
of each antenna with respect to the center of mass of the earth,
are determined a priori, by known methods, and preferably with
better fractional accuracy than is desired for the determinations
of the satellite orbits. Errors in the presumed knowledge of these
vectors will cause errors in the orbit determinations. However, as
discussed above with reference to the paper by Gerhard Beutler,
Werner Gurtner, Markus Rothacher, Thomas Schildknecht, and Ivo
Bauersima, entitled "Determination of GPS Orbits Using Double
Difference Carrier Phase Observations from Regional Networks",
appearing in the Proceedings of the Fourth International Geodetic
Symposium on Satellite Positioning, volume 1, pages 319-335,
published in 1986 by the Applied Research Laboratories of the
University of Texas at Austin, it is possible to refine the
position vectors of the stations simultaneously with the satellite
orbits. If this is to be done, appropriate a priori covariances
should be assigned to the uncertain station position
coordinates.
A composite of the signals simultaneously received from the
plurality of satellites by antenna 100 is applied to receiver 102
which converts the signals from the L1 and L2 bands of frequencies
at which the signals are received, to low frequencies at which the
operations of carrier reconstruction, phase measurement and
tracking are more conveniently performed. Frequency down-conversion
operations are performed within receiver 102 as disclosed in detail
hereinbelow with reference to FIG. 3, by heterodyning the received
signals with local oscillator signals. The oscillator signals are
synthesized by coherent multiplication of standard frequency signal
104 provided to receiver 102 by frequency standard 106. Carrier
reconstruction is also performed within receiver 102. As further
disclosed with reference to FIG. 3, a composite of reconstructed
carrier components, each related in phase and frequency to a
carrier implicit in the composite of spread spectrum signals
received by antenna 100, is formed in receiver 102. The
reconstructed carrier composite is sampled and the result, in
synchronous digital form, is carried by bus 110 to a plurality of
identical tracking channels 112. Bus 110 includes separate data
lines for the L1 and the L2 bands.
Frequency standard 106 is a stable reference standard, such as a
commercially available cesium atomic beam resonator controlled
oscillator. It has spectral purity sufficient to permit coherent
multiplication to L band, and long term stability and accuracy to
permit accurate time-keeping. Standard frequency signal 104 from
frequency standard 106 has a frequency equal to 2 f.sub.0, or 10.23
MHz.
In addition to being applied to receiver 102, standard frequency
signal 104 from frequency standard 106 is applied to and governs
the rate of clock 108. As disclosed in detail hereinbelow with
reference to FIGS. 3, 4, 5, and 6, clock 108 counts cycles of
standard frequency signal 104 to generate real time indication 124
which is applied to and governs the operation of computer 120 and
all of the tracking channels 112. Clock 108 of tracking station
STN-n is synchronized with the clocks of the other tracking
stations by means of synchronization signal 114 generated by
computer 120. (Preferably each station autonomously derives the
synchronization signal.) As mentioned above with reference to FIG.
1, synchronization signal 114 may be derived by any of a variety of
known methods, including decoding of the GPS signal modulation by
known means, not shown, included in receiver 102 and/or in one or
more of tracking channels 112.
The low frequency, digitized, composite of reconstructed carriers
output from receiver 102 on bus 110 is applied identically, in
parallel, to all of the tracking channels 112 where the phases of
the reconstructed carriers are individually measured. One tracking
channel 112 is assigned to each satellite, and selectively detects
only carriers from its assigned satellite, using satellite-specific
estimates 116 of the time-varying Doppler shift of the signals
received from that satellite.
Estimates 116 applied to tracking channels 112 by computer 120 are
computed by known methods from a priori information about the
satellite orbits and the tracking station position which may
conveniently be provided to computer 120 from the central processor
62 via data communication link 60. An alternative source of
information about the satellite orbits is the broadcast information
which is carried by the satellite signals and which may be read by
known methods involving knowledge of the GPS codes.
Data representing the results of carrier phase and related power
measurements performed within the tracking channels 112, indicated
in FIG. 2 as measurements 118, are provided to computer 120 which
may use these measurements to refine estimates 116 and, generally,
to monitor and control the measurement processes conducted within
the tracking channels. The measurements 118 are stored in the
memory of computer 120 until it is desired to transfer them to data
processor 62 (FIG. 1).
The transfer to processor 62 of the measurements 118 and related
data such as time tags derived from real time indication 124 from
clock 108, as well as other data related to the operation and
maintenance of station STN-32, uses modem 122, drop 128 and
communication link 60.
Data communication link 60 is bidirectional so that information
generated by data processor 62 relating to the satellite signals,
such as data representing Predictions of the frequencies of these
signals, may be transferred to computer 120 through modem 122 and
may be used by computer 120 to control or to aid the measurement
processes. In particular, estimates 116 applied to tracking
channels 112 may be derived partially or wholly from data received
by computer 120 from data processor 62 via line 60.
Computer 120 may also generate the clock synchronization signal
114, which is applied to clock 108 in order to initialize real time
indication 124, partially or wholly on the basis of data received
from data processor 62 via line 60. Alternatively, and as mentioned
above, the information necessary to synchronize clock 108 with the
clocks in all other stations and with a standard time such as "GPS"
time or Coordinated Universal Time, may be wholly or partially
derived from the satellite signals received at one of the stations
STN-n.
FIG. 3
The receiver 102 shown in FIG. 2 is illustrated in further detail
in FIG. 3. Receiver 102 accepts the L1 and L2 band signals
simultaneously received from the satellites by antenna 100. The
composite of spread spectrum signals received in each of these
bands is processed in receiver 102 to generate a composite of
reconstructed carrier signals. These L1- and L2-related,
reconstructed composite signals are also sampled in receiver 102,
and are applied in digital form via bus 110 to the identical
tracking channels 112 where individual satellites' reconstructed
carrier Phases are measured.
Reference frequency signal 104 from frequency standard 106 is
applied to receiver 102 where it governs the frequency
down-conversion and sampling operations which are performed in the
course of generating low frequency, digital signals on bus 110.
Receiver 102 receives the L band signals from antenna 100 via a
transmission line 150 which is coupled in turn to a preamplifier
assembly 152 including an L1 band pass filter 154, an L2 band pass
filter 156, and a low noise preamplification stage 158. A
transmission line 160 carries the filtered and preamplified signals
to a diplex filter 162 which supplies the L1 band signals to L1
sideband separator 168. This sideband separator also receives a
1575.42 MHz, L1 band center frequency reference signal 170
generated by a frequency multiplier 172 which is driven by
frequency standard 106 through line 104.
L1 sideband separator 168 generates separate upper and lower side
band outputs, 174 and 176 respectively, converted from the upper
and lower halves of the L1 band to lower frequencies by
heterodyning with L1 band center frequency reference signal 170. L1
upper sideband signal 174 and L1 lower sideband signal 176 are
filtered by L1 upper sideband filter 178 and L1 lower sideband
filter 180 respectively. A mixer 186 receives the outputs of these
filters and supplies their product to L1 22f.sub.0 in-phase sampler
190 and L1 2f.sub.0 quadrature sampler 192. These samplers are
synchronized by frequency standard 106 via line 104 in the case of
sampler 190, and via a 90 degree phase shifter 198 in the case of
sampler 192. The samplers, operating in relative quadrature, supply
inputs L1I and L1Q to the tracking channels via bus 110.
The L2 band section of the receiver is similarly organized and
includes L2 sideband separator 204, L2 upper sideband filter 210,
L2 lower sideband filter 212, mixer 218, L2 2f.sub.0 in-phase
sampler 222, and L2 2f.sub.0 quadrature sampler 224, all as
illustrated in FIG. 3.
Returning to the input section of the receiver, the spread-spectrum
composite of L1 and L2 band signals simultaneously received from
the plurality of satellites is carried from antenna 100 to
preamplifier assembly 152 by transmission line 150 which is made as
short as possible, preferably less than 1 meter long, in order to
minimize losses. Therefore preamplifier assembly 152 should be
mounted as close to antenna 100 as practicable with the antenna
having a clear view of the sky.
Preamplifier assembly 152 serve to amplify the received signals
sufficiently that these signals can be carried a moderately long
distance, e.g. via transmission line 160, from the location of
antenna 100 and preamplifier assembly 152, to the location of the
remaining portion of receiver 102 which may be relatively
remote.
Within preamplifier assembly 152 the signals received via
transmission line 150 are split and applied to the inputs of L1
band pass filter 154 and L2 band pass filter 156. These are high
quality, low loss band pass filters tuned to the L1 and L2
frequency bands, respectively. They are used to prevent any strong
out-of-band signals which may be picked up by antenna 100 from
reaching the low noise amplifier 158 and possibly burning it out or
overloading it or subsequent stages of receiver 102. To provide
power to the pre-amplifier, transmission line 160 may also carry
d.c. power from a power supply in receiver 102, not shown.
Diplex filter 162 is a frequency selective signal splitter which
separates the L1 band signals from the L2 band signals arriving via
transmission line 160, and outputs L1 band signals 164 and L2 band
signals 166 separately as shown. The L1 band signals 164 are
applied to the input of L1 sideband separator 168 and the L2 band
signals 166 are applied to the input of L2 sideband separator
204.
L1 sideband separator 168 may be configured conveniently as
described in detail in an article in the Proceedings of the IEEE,
vol. 59 (1971), pp. 1617-1618, by Alan E. E. Rogers, and further
described in United Kingdom Patent No. 2,120,489, published Feb.
26, 1986 and entitled "Method and system for determining position
using signals from satellites". L1 upper sideband signal 174 output
from L1 sideband separator 168 is a spread spectrum composite
representing that portion of L1 band signals 164 having frequencies
higher than 1575.42 MHz, the frequency of L1 center frequency
reference signal 170. The phase and the frequency of L1 center
frequency reference signal 170 are subtracted from the phases and
the frequencies of the Fourier components of the higher-frequency
half of the spectrum of L1 band signals 164 to obtain the phases
and the frequencies of the corresponding Fourier components of L1
upper sideband signal 174.
Similarly, L1 lower sideband signal 176 output from L1 sideband
separator 168 is a spread spectrum composite representing that
portion of L1 band signals 164 having frequencies lower than
1575.42 MHz, the frequency of L1 center frequency reference signal
170. The phases and the frequencies of the Fourier components of
the lower-frequency half of the spectrum of L1 band signals 164 are
subtracted from the phase and the frequency of L1 center frequency
reference signal 170 to obtain the phases and the frequencies of
the corresponding Fourier components of L1 lower sideband signal
176.
As previously noted, L1 upper and lower sideband signals 174 and
176 are applied to upper and lower sideband filters 178 and 180,
respectively. These two filters preferably have identical
properties. They are used to reject noise and any interfering
signals outside the useful range of frequencies in the upper and
lower sideband signals 174, 176. This range extends from about 10
kHz to about 9 MHz, except for a narrow band of frequencies
centered at f.sub.0, or 5.115 MHz. These filters should also
provide rejection at a frequency of 2f.sub.0, or 10.23 MHz.
Except for the rejection of frequencies below about 10 kHz and in a
"notch" centered at f.sub.0, the shape of each filter passband is
preferably matched to the shape of one sideband of the P-code
related component of a GPS signal. Thus, the filter has a
half-power bandwidth of about 4.5 MHz. The rejection of frequencies
below about 10 kHz prevents any L1 band signals received at
frequencies less than 10 kHz above or below the L1 band center
frequency from reaching mixer 186, where the second harmonics of
the 308 f.sub.0, L1 band center frequency carrier waves are
constructed. These carriers, as received, may have frequencies
differing from 308 f.sub.0 by up to about 5 kHz in either
direction, by virtue of Doppler shift. Their second harmonics are
Doppler-shifted by plus or minus up to 10 kHz. Thus the
low-frequency cutoffs of filters 178 and 180 prevent interference
with the reconstructed L1 band center frequency carriers.
Similarly, the notch centered at f.sub.0 in filters 178 and 180
prevents L1 band signals received at frequencies near 307 f.sub.0
and 309 f.sub.0 from interfering with the L1 band, f.sub.0
subcarriers. The second harmonics of these carriers are also
reconstructed in mixer 186. The frequencies of these reconstructed
second harmonics as they appear in L1 product 188 are near 2
f.sub.0, and differ from 2f.sub.0 by up to about 30 Hz in either
direction, due to Doppler shift. The range of frequencies of these
signals is relatively narrow, and the notches of filters 178 and
180 could be made equally narrow. However, it is more convenient to
provide much wider notches, of the order of 10 kHz or even 100 kHz
centered on 2f.sub.0. Even with the larger notch width, a
relatively small fraction of the desired signal power is lost since
this power is spread over a bandwidth of several MHz.
Except for narrow ranges of frequencies near the 10 kHz
low-frequency cutoff and the 5.115 MHz rejection notch, and for
frequencies beyond about 9 MHz where little signal power is found,
filters 178 and 180 should have phase shifts which are within a few
degrees of a linear function of frequency. In other words, the
filters should be nondispersive. This property is required for the
phase-coherent combination of spectral components from throughout
the useful frequency range, in the carrier reconstruction in mixer
186. Filters 178 and 180 having all the properties specified herein
may be configured using known techniques, for example by cascading
10 kHz high-pass and 5.115 MHz notch filters with a phase-linear
low-pass filter approximately matched to the P-code modulation
bandwidth.
The L1 product 188 which is generated by mixer 186 is applied to L1
2f.sub.0 in-phase sampler 190 and L1 2f.sub.0 quadrature sampler
192 as shown. L1 2f.sub.0 in-phase sampler 190 samples L1 product
188 at a uniform rate of 2f.sub.0, or 10.23 MHZ, in accordance with
standard frequency signal 104 received from frequency standard 106.
L1 2f.sub.0 quadrature sampler 192 also samples L1 product 188 at a
uniform rate of 2f.sub.0, or 10.23 MHz, in accordance with standard
frequency signal 104 received from frequency standard 106. However,
the phase of the sampling by L1 2f.sub.0 quadrature sampler 192
lags that of L1 2f.sub.0 in-phase sampler 190 because L1 2f.sub.0
quadrature sampler 192 is driven by quadrature sampling frequency
signal 148, generated by a 90.degree. phase shifter 198 which
delays standard frequency signal 104 by one-quarter cycle of
phase.
L1 2f.sub.0 in-phase sampler 190 generates L1 in-phase sampled
product 194 which is a digital signal, preferably including only
one bit per sample, to indicate just the sign. Similarly, L1
2f.sub.0 quadrature sampler 192 generates L1 quadrature sampled
product 196 which is of the same form. Limiting these sampled
products to one bit simplifies the subsequent digital signal
processing circuitry, while degrading the signal to noise ratios
tolerably. L1 in-phase sampled product 194 provides the "L1I" input
to each tracking channel 112, and L1 quadrature sampled product 196
provides the "L1Q" input to each tracking channel 112, as shown in
FIGS. 3 and 4. The L1 in-phase and quadrature sampled products 194
and 196 respectively, are carried, together with similar signals
from the L2 band section of receiver 102, via bus 110 to the
tracking channel 112.
The digital sampling rate, equal to 2f.sub.0, greatly exceeds the
frequencies of the reconstructed L1 center frequency carriers, all
less than 10 kHz, in L1 product 188. Thus, the frequencies and
phases of these reconstructed carriers are preserved in the
sampling process. The sampling rate of 2f.sub.0 is nominally
exactly equal to the second harmonic of the f.sub.0 carrier
implicit in the signals transmitted by each satellite. As received,
and after the frequency-doubling which occurs in the carrier
reconstruction process, these carriers have frequencies differing
from the 2f.sub.0 sampling rate by amounts between minus and plus
about 30 Hz. L1 2f.sub.0 in-phase sampler 190 and L1 2f.sub.0
quadrature sampler 192 act as mixers, subtracting the 2f.sub.0
sampling frequency from the reconstructed carrier frequencies near
2f.sub.0 to yield reconstructed carrier frequencies in L1 in-phase
sampled product 194 and L1 quadrature sampled product 196 in the
range from minus to plus 30 Hz. Note that negative frequencies are
distinct from positive frequencies in these sampled products
because the two samplers operate in phase quadrature.
In the preferred embodiment as illustrated in FIG. 3, the signal to
noise ratio of the reconstructed f.sub.0 carriers is degraded by
noise appearing in L1 product 188 at frequencies in the zero to 30
Hz range. Although the degradation is tolerable, performance of the
system can be improved if desired, by providing a separate pair of
quadrature samplers like L1 2f.sub.0 in-phase sampler 190 and L1
2f.sub.0 quadrature sampler 192, but connected to mixer 186 by a
band-pass filter tuned to the desired frequency band, centered at
2f.sub.0 in this case. These samplers and the related band-pass
filter, none of which is shown in FIG. 3, would be in addition to
those shown. The L1I and L1Q signals applied to 616 f.sub.0
detector 302 in tracking channel 112, disclosed below with
reference to FIG. 4, would continue to be derived from L1 2f.sub.0
in-phase sampler 190 and L1 2f.sub.0 quadrature sampler 192, as
shown. The added pair of samplers would drive L1 2f.sub.0 detector
304 (described hereinafter with reference to FIG. 4) in tracking
channel 112. Similar additions and changes could be made for the L2
section of receiver 102 and tracking channel 112.
As shown in FIG. 3, the L2 section of receiver 102 is organized
like the L1 section. L2 band signals 166 output by diplex filter
162 are applied to L2 sideband separator 204 which heterodynes
these signals with L2 center frequency reference signal 202. L2
center frequency reference signal 202 has a frequency of 240
f.sub.0, equal to 1227.60 MHz, and is derived from 2f.sub.0
standard frequency signal 104 by frequency multiplication in x120
frequency multiplier 200. Except for the difference in inputs, L2
sideband separator 204 operates exactly like, and may be
constructed exactly as, L1 sideband separator 168.
L2 sideband separator 204 generates separate L2 upper sideband
signal 206 and L2 lower sideband signal 208 outputs at baseband,
representing the upper and lower frequency halves of the spectrum
of the L2 band, just as disclosed above with reference to L1
sideband separator 168. The L2 upper and lower sideband signals
206, 208 are applied to L2 upper and lower sideband filters 210,
212, respectively. Except for the difference in inputs, these
filters operate exactly like, and may be constructed exactly as, L1
upper sideband filter 178 and L1 lower sideband filter 180.
Filtered L2 upper and lower sidebands signal 214 and 216, output
from the filters 210 and 212, respectively, are applied to mixer
218 which operates like mixer 186 in the L1 section of receiver
102. L2 product 220 output from mixer 218 is applied to L2 2f.sub.0
in-phase sampler 222 and L2 2f.sub.0 quadrature sampler 224 which,
again, are exactly like their counterparts in the L1 section: that
is, L1 2f.sub.0 in-phase sampler 190 and L1 2f.sub.0 quadrature
sampler 192. L2 in-phase sampler 222 samples L2 product 220 in
response to standard frequency signal 104, and L2 quadrature
sampler 224 samples L2 product 220 in response to quadrature
sampling frequency signal 148 which is derived, as mentioned above,
by delaying the phase of standard frequency signal 104 in
90.degree. phase shifter 198.
The output of the in-phase sampler 222 is L2 in-phase sampled
product 226, also labeled "L2I" in FIGS. 3 and 4. The output of
quadrature sampler 224 is L2 quadrature sampled product 228, also
labeled "L2Q" in FIGS. 3 and 4. In these outputs which are derived
from the signals received in the L2 band just as discussed above
for the L1-related signals, a plurality of reconstructed carrier
components is found, including both a reconstructed second harmonic
of the center frequency carrier and a reconstructed second harmonic
of the f.sub.0 subcarrier implicit in the L2 band signals from each
visible satellite. The reconstructed carriers are distinguished by
their different Doppler shifts. The Doppler shift of each carrier
is proportional to its frequency as transmitted, and to the rate of
change of the satellite-to-receiver range (sometimes called the
"range rate", or the "line-of-sight velocity").
FIG. 4
Referring now to FIG. 4, one of the plurality of identical tracking
channels 112 shown in FIG. 2 is illustrated in detail. As shown in
FIG. 4, tracking channel 112 includes a range generator 300 which
receives a satellite-specific range rate estimate 298, included in
estimates 116 from computer 120, and generates therefrom a 2f.sub.0
phase estimate 310 which is used by four synchronous detectors to
detect and measure the phases of four reconstructed carriers of the
particular satellite to which this tracking channel 112 is
assigned. These carriers are the L1 band center frequency carrier,
the L2 band center frequency carrier, the f.sub.0 subcarrier
implicit in the L1 band signals, and the f.sub.0 subcarrier
implicit in the L2 band signals.
L1 in-phase samPled product 194 and L1 quadrature sampled product
196 from receiver 102, received by tracking channel 112 via bus
110, are applied to 616 f.sub.0 detector 302 which detects the
second harmonic of the 308 f.sub.0, L1 band center frequency
carrier. The product signals 194, 196 are also applied to L1
2f.sub.0 detector 304 which detects the second harmonic of the
f.sub.0, L1 band subcarrier. Similarly, L2 in-phase sampled product
226 and L2 quadrature sampled product 228 from receiver 102, also
received by tracking channel 112 via bus 110, are applied to 480
f.sub.0 detector 306 which detects the second harmonic of the 240
f.sub.0, L2 band center frequency carrier, and also to L2 2f.sub.0
detector 308 which detects the second harmonic of the f.sub.0, L2
band subcarrier.
Each of the four synchronous detectors in tracking channel 112 also
receives an estimate of the time-varying phase of the particular
carrier which it is supposed to detect, and each produces a
measurement of the difference between the actual carrier phase and
the estimate of this phase. All four carrier phase estimates, one
for each carrier to be detected, are derived by multiplying
2f.sub.0 phase estimate 310, generated by range generator 300 from
range rate estimate 298, by appropriate factors. This is
appropriate since all four carriers were generated from the same
fundamental frequency source within the same satellite, and since
all have equal fractional frequency shifts due to the Doppler
effect. The 2f.sub.0 phase estimate 310 is applied directly, that
is without multiplication, to L1 2f.sub.0 detector 304 and L2
2f.sub.0 detector 308. The same 2f.sub.0 phase estimate 310 is
multiplied by a factor of 308 in .times.308 multiplier 312 whose
output, estimate 314, is applied to 616 f.sub.0 detector 302. The
same 2f.sub.0 phase estimate 310 is multiplied by a factor of 240
in .times.240 multiplier 316 whose output, estimate 318, is applied
to 480 f.sub. 0 detector 306.
The 616 f.sub.0 detector 302 produces 616 f.sub.0 residual phase
measurement 320, a measurement of the difference between the actual
phase of the reconstructed, second harmonic, L1 center frequency
carrier of the selected satellite and the 616 of the f.sub.0
carrier implicit in the signals transmitted by each f.sub.0 phase
estimate 314.
L1 2f.sub.0 detector 304 produces L1 2f.sub.0 residual phase
measurement 322, a measurement of the difference between the actual
phase of the reconstructed, second harmonic, L1 band f.sub.0
subcarrier of the selected satellite and the 2f.sub.0 phase
estimate 310.
The 480 f.sub.0 detector 306 produces 480 f.sub.0 residual phase
measurement 324, a measurement of the difference between the actual
phase of the reconstructed, second harmonic, L2 center frequency
carrier of the selected satellite and the 480 f.sub.0 phase
estimate 318.
L2 2f.sub.0 detector 308 produces L2 2f.sub.0 residual phase
measurement 326, a measurement of the difference between the actual
phase of the reconstructed, second harmonic, L2 band f.sub.0
subcarrier of the selected satellite and the 2f.sub.0 phase
estimate 310.
Each of the four synchronous detectors also produces a measurement
of the power of the related carrier. Thus, 616 f.sub.0 detector 302
produces L1 center frequency carrier power measurement 330; L1
2f.sub.0 detector 304 produces L1 subcarrier power measurement 332;
480 f.sub.0 detector 306 produces L2 center frequency carrier power
measurement 334; and L2 2f.sub.0 detector 308 produces L2
subcarrier power measurement 336.
Each synchronous detector, such as 616 f.sub.0 detector 302 which
detects the reconstructed, second harmonic, L1 center frequency
carrier of the selected satellite, selectively detects the signal
received from the selected satellite and rejects signals from other
satellites because, virtually always, the desired satellite's
reconstructed carrier signal differs in frequency from the
undesired satellite's. Each synchronous detector responds only to
input signal frequencies which are very near to the frequency, that
is the rate, of the related carrier phase estimate, such as 616
f.sub.0 phase estimate 314 which is supplied to 616 f.sub.0
detector 302.
The phase estimate supplied to each synchronous detector is applied
within the detector to the input signals, such as L1I and L1Q, in
order to subtract the phase estimate from the phases of the input
signals. As discussed above with reference to FIG. 3, the input
signals include a plurality of reconstructed carrier components,
from all visible satellites. One of these input signal components,
the desired component, has phase varying with time at very nearly
the same rate as the phase estimate. Following the subtraction of
the phase estimate from the composite signal, the phase of the
desired component is therefore virtually static, so this signal
component may be distinguished from noise and other signals by
integrating the composite signal for an interval of time. Such an
integration is performed within each synchronous detector, such as
the 616 f.sub.0 detector 302, as disclosed further below with
reference to FIG. 5.
In order for this method of signal selection to work, of course,
the rate of the phase estimate applied to the synchronous detector
must match the phase rate, or frequency, of the desired signal
component sufficiently accurately. Because range rate estimate 298
from computer 120 might not be sufficiently accurate, range
generator 300 also receives an input from 616 f.sub.0 residual
phase measurement 320 which serves as an error signal and is
applied in range generator 300 to correct 2f.sub.0 phase estimate
310. Thus a closed feedback loop is formed which includes the range
generator 300, the .times.308 multiplier 312, and the 616 f.sub.0
detector 302. This loop acts as a phase-locked tracking loop to
track the phase of the L1 center frequency carrier of the signals
received from the selected satellite.
Only the L1 center frequency carrier, not the other carriers
reconstructed from the received signals, is tracked within tracking
channel 112; and the 2f.sub.0 phase estimate 310 which is
phase-locked to this carrier is, or is the basis for, the phase
estimate applied to each of the four synchronous detectors in
tracking channel 112. It is preferred to base all the carrier phase
estimates for a given satellite on the L1 center frequency carrier
because the signal-to-noise ratio of this reconstructed carrier is
the highest. However, a working system could be constructed in
which the phase estimates were derived in other ways.
The four carrier power measurements, L1 center frequency carrier
power measurement 330, L1 subcarrier power measurement 332, L2
center frequency carrier power measurement 334, and L2 subcarrier
power measurement 336, are included in measurements 118 along with
2f.sub.0 phase estimate 310 and the four residual phase
measurements: 616 f.sub.0 residual phase measurement 320, L1
2f.sub.0 residual phase measurement 322, 480 f.sub.0 residual phase
measurement 324, and L2 2f.sub.0 residual phase measurement 326.
The latter measurements are called "residual" phase measurements
because each represents only the residual, or difference, between
the related actual and estimated carrier phase. Addition of each
residual phase measurement value to the related phase estimate
yields the total value of the "one-way phase" measurement for the
related carrier. Such additions are conveniently performed in
computer 120, although they might also be performed in central data
processor 62.
FIG. 5
To further describe the detectors, the 616 f.sub.0 detector 302 is
shown in detail in FIG. 5. It is convenient to construct all four
detectors identically although the preferred value of signal
integration time is not the same for all four. As discussed
hereinbelow, the preferred integration time for 616 f.sub.0
detector 302 is 1 second, whereas the preferred integration time
for detectors 304, 306 and 308 is 100 seconds.
While the construction and operation of the other detectors may be
understood from the descriPtion of detector 302, a subtle
difference should be noted between the operations of the two center
frequency carrier detectors (616 f.sub.0 detector 302 and 480
f.sub.0 detector 306) on one hand, and the two subcarrier detectors
(L1 2f.sub.0 detector 304 and L2 2f.sub.0 detector 308) on the
other. This difference arises not from any differences between the
detectors themselves, but from a difference between the center
frequency carriers and the subcarriers as they appear in the I and
Q inputs.
As mentioned above with reference to FIG. 3, the reconstructed
center frequency carriers appear with frequencies in the range from
zero to about 10 kHz in L1 product 188. The frequency of a
reconstructed center frequency carrier in L1 product 188 is equal
to twice the magnitude (i.e., twice the absolute value) of the
Doppler shift of the related, 308 f.sub.0, L1 band center frequency
carrier. Positive and negative Doppler shifts of equal magnitude
yield the same frequency in L1 product 188. A consequence of this
Doppler "imaging" is a 3 dB loss of signal to noise ratio (SNR). A
less important consequence is the possibility of interference
between two satellites having equal magnitude, opposite Doppler
shifts. Such interference occurs in practice but so rarely, and so
briefly, that it can be ignored. The imaging and the consequent SNR
loss could be eliminated by the addition of a quadrature
counterpart of mixer 186 in receiver 102. Actual experience has
shown such an addition to be unnecessary, so it is omitted from the
preferred system disclosed herein.
Closely related to the occurrence of center frequency Doppler
"imaging" is the fact that each reconstructed center frequency
carrier appears with virtually the same phase in both L1I and L1Q.
This is contrary to what one expects in a pair of signals labeled
"I" and "Q".
The reconstructed f.degree. subcarriers, unlike the reconstructed
center frequency carriers, do not suffer from Doppler imaging in
the "I" and "Q" signals from receiver 102. Each reconstructed
subcarrier signal appears in Q with phase differing by 90.degree.
from its phase in I. The sense of this phase difference, leading or
lagging, depends on whether the Doppler shift is positive or
negative. Thus, I and Q Provide a rotating "phasor" description of
a reconstructed subcarrier signal.
The phasor concept is helpful to understanding the operations of
all the synchronous detectors, and will be used in the following
description of the operation of the 616 f.sub.0 detector 302
despite the fact that the phasor representing the reconstructed L1
center frequency carrier signal does not properly rotate about the
origin of the I-Q plane; rather, it oscillates on a line of unit
slope. It will be recalled that such a linearly oscillating phasor
is the sum of two rotating phasors of equal magnitude, with equal
rotation rates, rotating in opposite directions. The 616 f.sub.0
detector 302 responds to one of these phasors and rejects the
other, just as it rejects phasors of other satellites. In the
following description of detector operation the rejected phasor
will be ignored. Thus, the same description can be taken to apply
to all four detectors.
By way of briefly summarizing the description to this point, the
616 f.sub.0 detector 302 receives as inputs from receiver 102, L1
in-phase sampled product 194, "L1I", and L1 quadrature sampled
product 196, "L1Q". L1I and L1Q were generated in the receiver 102
by sampling L1 product 188 from mixer 186 as shown in FIG. 3.
Present in both L1I and L1Q is a composite of reconstructed carrier
signals, simultaneously including signals from all visible
satellites. The reconstructed center frequency carrier of the L1
band signal received from the particular satellite to which
tracking channel 112 has been assigned is selected by the 616
f.sub.0 detector 302. The selection is based on an estimate of the
time-varying phase of this specific carrier encoded in 616 f.sub.0
phase estimate 314 which is generated by .times.308 multiplier 312.
Both 2f.sub.0 phase estimate 310 and 616 f.sub.0 phase estimate 314
are binary digital signals, and .times.308 multiplier 312 is a
digital multiplier.
The 2f.sub.0 phase estimate 310 which is generated by range
generator 300 is updated at a fixed rate of 2f.sub.0 /93, or
exactly 110 KHz, in accordance with 2f.sub.0 standard frequency
signal 104 from frequency standard 106 and real time indication 124
from clock 108 (FIGS. 2, 3). The .times.308 multiplier 312 operates
to update 616 f.sub.0 phase estimate 314 at the same rate.
It is convenient to derive a 2f.sub.0 /93 synchronous "clock"
signal for controlling the phase estimate generation and related
multiplications, by dividing 2f.sub.0 standard frequency signal 104
by factors of 31 and 3 by means of digital dividers included in
clock 108 but not shown in FIG. 2. Further divisions, first by a
factor of 11 and then by successive factors of 10, yield a digital
representation of the time in decimal seconds. The clock signals
corresponding to the 1-second and the 100-second decimal digits are
used to control integration functions performed within synchronous
detectors 302, 304, 306, and 308 as described above with reference
to FIG. 4 and below with reference to FIG. 5.
As shown in FIG. 5, the 616 f.sub.0 phase estimate 314 is applied
to the I and Q signals, (L1 in-phase sampled product 194 and L1
quadrature sampled product 196), in quadrant rotation logic 400.
From these three digital input signals, quadrant rotation logic 400
generates another pair of digital "I" and "Q" signals, in-phase
rotated signal 402 and quadrature rotated signal 404.
As will be recalled, each of L1 in-phase sampled product 194 and L1
quadrature sampled product 196 is a one-bit digital signal. The two
bits taken together indicate the quadrant of the phasor
representing the composite of all the reconstructed L1 carriers.
Similarly, each of in-phase rotated signal 402 and quadrature
rotated signal 404 is a one-bit digital signal. These two bits
taken together also indicate the quadrant of a phasor representing
the composite of all the reconstructed L1 carriers. However, the
latter phasor is rotated with respect to the former phasor, through
the action of quadrant rotation logic 400, by an angle equal
(modulo 360 degrees) to 616 f.sub.0 phase estimate 314.
As mentioned, 616 f.sub.0 phase estimate 314 represents phase in
the form of a binary number. The unit of this representation is one
cycle of phase. The first two bits to the right of the binary point
therefore indicate the quadrant of 616 f.sub.0 phase estimate 314.
These two bits of 616 f.sub.0 phase estimate 314 are combined with
the two bits of L1 in-phase sampled product 194 and L1 quadrature
sampled product 196 in quadrant rotation logic 400 to generate the
two output bits, in-phase rotated signal 402 and quadrature rotated
signal 404. This logic must operate at a clock rate of 2f.sub.0,
the rate of the one-bit I & Q signal inputs. The truth table of
this logic may readily be completed from the foregoing description,
and is given in the U. S. patent application entitled "METHOD AND
SYSTEM FOR DETERMINING POSITION ON A MOVING PLATFORM, SUCH AS A
SHIP, USING SIGNALS FROM GPS SATELLITES", Ser. No. 852016, filed on
Apr. 14, 1986 in the name of Charles C. Counselman III.
In-phase rotated signal 402 is integrated for an interval of time
to distinguish the selected signal component from the noise and
other components present in the composite, by means of clocked
counter 410. Similarly, quadrature rotated signal 404 is integrated
by means of clocked counter 420. The two counters are identical in
construction and operation. The integrations by these counters are
started and stopped by real time indication 124 from clock 108. As
mentioned above, the integration time interval is 1 second in the
case of 616 f.sub.0 detector 302, and 100 seconds for the other
three detectors in tracking channel 112. In 616 f.sub.0 detector
302, an integration begins every second on the second. At these
times clocked counter 410 and clocked counter 420 are reset to zero
and commence counting. Each counter is clocked by standard
frequency signal 104 from frequency standard 106. On every cycle of
this 2f.sub.0 clock signal, each counter is incremented if and only
if its input, in-phase rotated signal 402 for clocked counter 410
and quadrature rotated signal 404 for clocked counter 420, is TRUE.
At the end of the integration time interval, the accumulated count
in clocked counter 410 is read out as inphase accumulation 412, and
the accumulated count in clocked counter 420 is read out as
quadrature accumulation 422.
In-phase accumulation 412 and quadrature accumulation 422 taken
together form the address used to read a memory in which two
precomputed numerical tables are stored. From arctangent table 430,
the value of 616 f.sub.0 residual phase measurement 320 is read,
and from root-sum-of-squares table 440, the value of L1 center
frequency carrier power measurement 330 is read. These values are
included in measurements 118 which are passed from tracking channel
112 to computer 120 as shown in FIGS. 2 and 4.
The theory of operation of the clocked counters 410 and 420 and the
tables 430 and 440 are explained in the aforementioned U.S. patent
application entitled "METHOD AND SYSTEM FOR DETERMINING POSITION ON
A MOVING PLATFORM, SUCH AS A SHIP, USING SIGNALS FROM GPS
SATELLITES", Ser. No. 852,016, filed on Apr. 14, 1986, which
application is a continuation-in-part of the U.S. patent
application entitled "METHOD AND SYSTEM FOR MEASURING BASELINE
VECTORS BY RADIO INTERFEROMETRY USING RADIO SIGNALS FROM GPS
SATELLITES", Ser. No. 353,331, filed on Mar. 1, 1982, both in the
name of Charles C. Counselman III.
An explanation of the operation of similar clocked counters and
arctangent and root-sum of-squares tables in a system very similar
to 616 f.sub.0 detector 302 is also given in United Kingdom Patent
No. 2,120,489, published Feb. 26, 1986 and entitled "Method and
system for determining position using signals from satellites".
Comparison of the system illustrated in United Kingdom Patent No.
2,120,489 with the system illustrated in FIG. 5 herein shows that
the two systems are equivalent except for the inclusion of L1
quadrature sampled product 196 and related logic in quadrant
rotation logic 400.
FIG. 6
The range generator 300 shown in FIG. 4 is illustrated in further
detail in FIG. 6. As shown in these Figures, range generator 300
receives satellite-specific range rate estimate 298 from computer
120 and generates 2f.sub.0 phase estimate 310 which is applied
directly or indirectly to all four synchronous detectors in
tracking channel 112. The 2f.sub.0 phase estimate 310 is applied
directly to detectors 304 and 308, to detector 302 via .times.308
multiplier 312, and to detector 306 via the .times.240 multiplier
316. In the quadrant rotation logic 400 within each detector, the
relevant phase estimate is used to rotate the input
composite-signal phasor at just the right rate to counter, and
stop, the rotation of the particular phasor component representing
the carrier component which is to be detected.
As shown in FIG. 6, range generator 300 includes two digital
registers, range register 450 and rate register 460. Range register
450 contains a binary number representing a biased estimate of
range between the antenna 100 of tracking station STN-n, and the
particular satellite, such as GPS-12, to which this tracking
channel 112 is assigned. The range is represented in units equal to
one wavelength at a frequency of 2f.sub.0, approximately 29 meters.
Range register 450 is a 58-bit binary register with 20 bits to the
left and 38 bits to the right of the binary point. The number
contained in range register 450 is 2f.sub.0 phase estimate 310. As
disclosed above with reference to FIGS. 4 and 5, just the first two
bits to the right of the binary point of this number are applied
directly to the quadrant rotation logic 400 in L1 2f.sub.0 detector
304 and L2 2f.sub.0 detector 308. Twelve or more bits to the right
of the binary point of 2f.sub.0 phase estimate 310 are needed by
.times.308 multiplier 312 and .times.240 multiplier 316 in order to
generate 616 f.sub.0 phase estimate 314 and 480 f.sub.0 phase
estimate 318, respectively, with sufficient precision. Sixteen or
more bits to the right, and 20 bits to the left of the binary point
of 2f.sub.0 phase estimate 310 are included in the measurements 118
output to computer 120 as shown in FIGS. 2, 4, and 6.
As mentioned above, 2f.sub.0 phase estimate 310 is updated at a
uniform rate 110,000 times per second. At this rate, the number
(2f.sub.0 phase estimate 310) in range register 450 is replaced
with the sum, computed in adder 470, of 2f.sub.0 phase estimate 310
plus range increment 462 which is contained in rate register 460.
Once per second, a new value of 616 f.sub.0 residual phase
measurement 320 is received from 616 f.sub.0 detector 302, is
rescaled in scale converter 464, and the result is added into the
sum formed by adder 470.
Range increment 462 represents the time rate of change of 2f.sub.0
phase estimate 310 in units equal to 110,000 kHz, that is, 110,000
cycles of phase per second. Like range register 450, rate register
460 and adders 468 and 470 require 38 bits to the right of the
binary point. However, rate register 460 and adder 468 need have no
bits to the left of the binary point.
As disclosed above with reference to FIG. 4, the addition once per
second of a scaled value of 616 f.sub.0 residual phase measurement
320 into 2f.sub.0 phase estimate 310 is part of a feedback control
process which causes 2f.sub.0 phase estimate 310 to track the L1
band center frequency carrier phase. It would be natural for scale
converter 464 to divide 616 f.sub.0 residual phase measurement 320
by a factor of 308. However, it is simpler, and acceptable since
only an error signal is being processed at this stage, for scale
converter 464 just to shift 616 f.sub.0 residual phase measurement
320 by 8 bits to the right. This shift is equivalent to division by
256.
The feedback process is also effected by adding 616 f.sub.0
residual phase measurement 320, after scaling by scale converter
466, into rate register 460 by means of adder 468. Ten times per
second, the value (i.e., range increment 462) in rate register 460
is replaced by the sum, formed in adder 468, of the current value
in rate register 460 and the value of range rate estimate 298
received from computer 120. Once per second, the scaled value of
616 f.sub.0 residual phase measurement 320 is also added into this
sum. Since phase tracking errors, represented by 616 f.sub.0
residual phase measurement 320, are accumulated in rate register
460 whose contents are further accumulated in range register 450,
the feedback loop is a second-order loop. The loop dynamics, such
as the transient response and bandwidth, are determined by the
scale factors applied to 616 f.sub.0 residual phase measurement 320
in scale converter 464 and scale converter 466. The optimal value
of loop bandwidth, given the stability of the frequency standards
of the existing GPS satellites, is equal to about 0.5 Hz. To set
the bandwidth, the scale factor applied in scale converter 466 may
be set in accordance with known techniques of feedback control.
The phase locked loop is rate-aided by computer 120 which furnishes
an updated range rate estimate 298 ten times per second to adder
468. Range rate estimate 298 represents the amount by which range
increment 462 is expected to change each 0.1 second. Thus, range
rate estimate 298 represents a prediction of the acceleration of
2f.sub.0 phase estimate 310. In order to load an initial range
increment 462 into rate register 460, a path 458 bypassing adder
468 is provided.
* * * * *